This series consists of weekly discussion sessions on foundations of quantum Theory and quantum information theory. The sessions start with an informal exposition of an interesting topic, research result or important question in the field. Everyone is strongly encouraged to participate with questions and comments. http://pirsa.org/podcast/S006 Science 2012 http://blogs.law.harvard.edu/tech/rss en-ca Thu, 09 Feb 2012 04:24:29 -0500 sbradwell@perimeterinstitute.ca Thu, 09 Feb 2012 04:24:29 -0500 G 180 sbradwell@perimeterinstitute.ca Steve Bradwell's - Podcast Generator Ernesto Galvao http://streamer.perimeterinstitute.ca/mp3/289fcbe3-3f30-4900-84ff-26120585f6e1.mp3 Science http://streamer.perimeterinstitute.ca/mp3/289fcbe3-3f30-4900-84ff-26120585f6e1.mp3 Wed, 06 Oct 2004 16:00:00 -0400 Robert Spekkens http://streamer.perimeterinstitute.ca/mp3/df9cb554-ff43-4819-a290-707adb0bce00.mp3 Science http://streamer.perimeterinstitute.ca/mp3/df9cb554-ff43-4819-a290-707adb0bce00.mp3 Wed, 27 Oct 2004 16:00:00 -0400 Matthew Leifer http://streamer.perimeterinstitute.ca/mp3/802fca00-a56e-4fdd-ad96-3c96b1c2ae2f.mp3 Science http://streamer.perimeterinstitute.ca/mp3/802fca00-a56e-4fdd-ad96-3c96b1c2ae2f.mp3 Wed, 10 Nov 2004 16:00:00 -0500 Ivette Fuentes http://streamer.perimeterinstitute.ca/mp3/31b81ba7-0891-47a0-bd89-5229ae81d5ce.mp3 Science http://streamer.perimeterinstitute.ca/mp3/31b81ba7-0891-47a0-bd89-5229ae81d5ce.mp3 Wed, 17 Nov 2004 15:55:00 -0500 Steven Weinberg http://streamer.perimeterinstitute.ca/mp3/e4051e48-91d4-4231-a34a-a3a4abe9793f.mp3 Science http://streamer.perimeterinstitute.ca/mp3/e4051e48-91d4-4231-a34a-a3a4abe9793f.mp3 Wed, 24 Nov 2004 15:50:00 -0500 Enrique Rico-Ortega http://streamer.perimeterinstitute.ca/mp3/037495b2-8662-4d9e-beb1-3e22ef720abb.mp3 Science http://streamer.perimeterinstitute.ca/mp3/037495b2-8662-4d9e-beb1-3e22ef720abb.mp3 Wed, 19 Jan 2005 16:00:00 -0500 Guife Vidal http://streamer.perimeterinstitute.ca/mp3/0e9cb190-15a7-430d-a4ab-bcfd60a15fe8.mp3 Science http://streamer.perimeterinstitute.ca/mp3/0e9cb190-15a7-430d-a4ab-bcfd60a15fe8.mp3 Wed, 02 Feb 2005 15:50:00 -0500 Robert Alicki http://streamer.perimeterinstitute.ca/mp3/cbef072b-a431-4668-8f06-9935da17d322.mp3 Science http://streamer.perimeterinstitute.ca/mp3/cbef072b-a431-4668-8f06-9935da17d322.mp3 Wed, 23 Feb 2005 16:00:00 -0500 Anthony Aguirre http://streamer.perimeterinstitute.ca/mp3/f50ac504-12c9-41b4-9612-33193464ed63.mp3 Science http://streamer.perimeterinstitute.ca/mp3/f50ac504-12c9-41b4-9612-33193464ed63.mp3 Mon, 28 Feb 2005 11:00:00 -0500 Understanding how galaxies form is a major current goal in physical cosmology: although a basic picture is well-accepted, there are outstanding mysteries to be solved. First, what is the origin of the heavy elements seen outside of galaxies? Given that these elements are created only inside galaxies, there must be a process whereby galaxies can expel gas rather than accrete it. Second, galaxy properties are somewhat different from theory predicts, yet extremely regular -- to the extent that it has been seriously argued that modified gravity, rather than dark matter, explains them. I will discuss these mysteries and the possibility that the same culprit -- galactic winds -- may play a key role in solving both. Anthony Aguirre http://streamer.perimeterinstitute.ca/mp3/e66a4e1f-289b-49d0-ad1e-038922bfcfdb.mp3 Science http://streamer.perimeterinstitute.ca/mp3/e66a4e1f-289b-49d0-ad1e-038922bfcfdb.mp3 Tue, 01 Mar 2005 16:00:00 -0500 J.C Boileau http://streamer.perimeterinstitute.ca/mp3/6e0e8e7e-61aa-4e6f-a909-c561eafde13b.mp3 Science http://streamer.perimeterinstitute.ca/mp3/6e0e8e7e-61aa-4e6f-a909-c561eafde13b.mp3 Wed, 09 Mar 2005 16:05:00 -0500 One of the central critical results in the theory of fault-tolerant quantum computation is that arbitrarily long reliable computation is possible provided the error rate per gate and per time step is below some threshold value. This was proved by a number of groups, but the detailed published proofs are complex and furthermore only hold for concatenation of quantum error-correcting codes able to correct 2 errors per block, while typically the best estimates of the threshold value are based on the 7-qubit code, which only corrects 1 error per block. I will describe recent work by Panos Aliferis, John Preskill, and myself which substantially simplifies existing proofs and applies as well to the concatenated 7-qubit code. The new proof also provides a nice framework in which to attempt to prove relatively high values of the threshold, which so far have only emerged as estimates from simulations Daniel Gottesman http://streamer.perimeterinstitute.ca/mp3/38786db3-eb76-4999-b2c8-873b584ba4f1.mp3 Science http://streamer.perimeterinstitute.ca/mp3/38786db3-eb76-4999-b2c8-873b584ba4f1.mp3 Wed, 23 Mar 2005 16:00:00 -0500 Kaustubh Agashe http://streamer.perimeterinstitute.ca/mp3/ccdc10c4-97da-4bc4-8b5a-36d83c8365b6.mp3 Science http://streamer.perimeterinstitute.ca/mp3/ccdc10c4-97da-4bc4-8b5a-36d83c8365b6.mp3 Thu, 24 Mar 2005 16:00:00 -0500 Valerio Scarani http://streamer.perimeterinstitute.ca/mp3/7c94e7d8-6f20-42a3-a923-dfa1bcbf37ce.mp3 Science http://streamer.perimeterinstitute.ca/mp3/7c94e7d8-6f20-42a3-a923-dfa1bcbf37ce.mp3 Wed, 06 Apr 2005 16:00:00 -0400 Seth Lloyd http://streamer.perimeterinstitute.ca/mp3/7a92bc77-44a5-4651-ab50-a63d68c4ad7d.mp3 Science http://streamer.perimeterinstitute.ca/mp3/7a92bc77-44a5-4651-ab50-a63d68c4ad7d.mp3 Tue, 12 Apr 2005 16:00:00 -0400 Fabio Benatti http://streamer.perimeterinstitute.ca/mp3/5450b3fd-5de7-4f61-8487-a680cd1e283d.mp3 Science http://streamer.perimeterinstitute.ca/mp3/5450b3fd-5de7-4f61-8487-a680cd1e283d.mp3 Wed, 20 Apr 2005 16:00:00 -0400 In this talk I'll discuss recent joint work with Raymond Laflamme, David Poulin and Maia Lesosky in which a unified approach to quantum error correction is presented, called "operator quantum error correction". This scheme relies on a generalized notion of noiseless subsystems and includes the known techniques for the error correction of quantum operations --i.e., the standard model, the method of decoherence-free subspaces, and the noiseless subsystem method--as special cases. Correctable codes in this approach take the form of operator algebras and operator semigroups. The condition from the standard model is shown to be necessary for all of the known methods of error correction, and we'll see this as part of a discussion on conditions that characterize correctability for the general case. David Kribs http://streamer.perimeterinstitute.ca/mp3/05296fd7-d64a-4756-87a8-470296144848.mp3 Science http://streamer.perimeterinstitute.ca/mp3/05296fd7-d64a-4756-87a8-470296144848.mp3 Tue, 24 May 2005 04:00:00 -0400 Rainer Verch http://streamer.perimeterinstitute.ca/mp3/92257ecc-d69e-46dd-8842-ceddbe609ac1.mp3 Science http://streamer.perimeterinstitute.ca/mp3/92257ecc-d69e-46dd-8842-ceddbe609ac1.mp3 Wed, 01 Jun 2005 16:00:00 -0400 David Poulin http://streamer.perimeterinstitute.ca/mp3/317f4964-c7a0-4e39-8b13-2a6c252ceb05.mp3 Science http://streamer.perimeterinstitute.ca/mp3/317f4964-c7a0-4e39-8b13-2a6c252ceb05.mp3 Wed, 08 Jun 2005 04:00:00 -0400 Daniel Lidar http://streamer.perimeterinstitute.ca/mp3/da6880df-b844-47d7-a339-c2d96423583c.mp3 Science http://streamer.perimeterinstitute.ca/mp3/da6880df-b844-47d7-a339-c2d96423583c.mp3 Wed, 15 Jun 2005 04:00:00 -0400 Simon Saunders http://streamer.perimeterinstitute.ca/mp3/cef238a6-742c-4775-8ce6-fca219827b95.mp3 Science http://streamer.perimeterinstitute.ca/mp3/cef238a6-742c-4775-8ce6-fca219827b95.mp3 Wed, 03 Aug 2005 16:00:00 -0400 David Deutsch http://streamer.perimeterinstitute.ca/mp3/d9e577f5-031a-41af-8544-ea1cc4209077.mp3 Science http://streamer.perimeterinstitute.ca/mp3/d9e577f5-031a-41af-8544-ea1cc4209077.mp3 Wed, 24 Aug 2005 16:00:00 -0400 Choi http://streamer.perimeterinstitute.ca/mp3/5acdde0a-a814-47f0-9bbb-2ffbfac9b394.mp3 Science http://streamer.perimeterinstitute.ca/mp3/5acdde0a-a814-47f0-9bbb-2ffbfac9b394.mp3 Wed, 21 Sep 2005 16:00:00 -0400 Hans Westman,Ward Struyve http://streamer.perimeterinstitute.ca/mp3/04b09045-5276-42ad-be44-65d8dbe2166b.mp3 Science http://streamer.perimeterinstitute.ca/mp3/04b09045-5276-42ad-be44-65d8dbe2166b.mp3 Wed, 28 Sep 2005 16:00:00 -0400 Garnet Ord http://streamer.perimeterinstitute.ca/mp3/01a99ea2-1d23-4eb9-b7f0-b5dc3ae3cd13.mp3 Science http://streamer.perimeterinstitute.ca/mp3/01a99ea2-1d23-4eb9-b7f0-b5dc3ae3cd13.mp3 Wed, 05 Oct 2005 15:30:00 -0400 I shall discuss entanglement - assisted invariance (symmetry exhibited by correlated quantum states) and describe how it can be used to understand the nature of ignorance, and, hence, the origin of probabilities in quantum physics. WHZ, Phys. Rev. Lett. 90, 120404 (2003); Rev. Mod. Phys. 75, 715 (2003); Phys. Rev. 71, 052105 (2005) (quant-ph/0405161). Wojciech Zurek http://streamer.perimeterinstitute.ca/mp3/36145b3f-0869-40ce-ab23-2ec32642f038.mp3 Science http://streamer.perimeterinstitute.ca/mp3/36145b3f-0869-40ce-ab23-2ec32642f038.mp3 Wed, 09 Nov 2005 16:00:23 -0500 Optical experiments led the way to quantum information with striking examples of Bell's inequality tests and entangled state synthesis. Early demonstrations of quantum communication proved that optics are important for quantum communication and more recent ideas about linear optic quantum computing raised hopes that this would also be true for computing. I will give an overview of the various elements that are required for optical QIP and the state-of-the-art characteristics. I will then specialize on sources of single photons and entangled photon pairs and show how they need to be adapted to the task at hand. Gregor Weihs http://streamer.perimeterinstitute.ca/mp3/3840fc6e-fc02-4be2-b464-4c422c90c865.mp3 Science http://streamer.perimeterinstitute.ca/mp3/3840fc6e-fc02-4be2-b464-4c422c90c865.mp3 Wed, 23 Nov 2005 16:00:54 -0500 Bohr’s Principle of Complementarity of wave and particle aspects of quantum systems has been a cornerstone of quantum mechanics since its inception. Einstein, Schrödinger and deBroglie vehemently disagreed with Bohr for decades, but were unable to point out the error in Bohr’s arguments. I will report three recent experiments in which Complementarity fails, and argue that the results call for an upgrade of the Quantum Measurement theory. Finally, I will introduce the novel concept of Contextual Null Measurement (CNM) and discuss some of its surprising applications. Web-page: users.rowan.edu/~afshar/ Preprint (published in Proc. SPIE 5866, 229-244, 2005): http://www.irims.org/quant-ph/030503/ Shahriar S. Afshar http://streamer.perimeterinstitute.ca/mp3/bcac7f63-03c4-4029-892a-97510d984699.mp3 Science http://streamer.perimeterinstitute.ca/mp3/bcac7f63-03c4-4029-892a-97510d984699.mp3 Wed, 30 Nov 2005 16:00:15 -0500 will discuss how to realize, by means of non-abelian quantum holonomies, a set of universal quantum gates acting on decoherence-free subspaces and subsystems. In this manner the quantum coherence stabilization virtues of decoherence-free subspaces and the fault-tolerance of all-geometric holonomic control are brought together. Paolo Zanardi http://streamer.perimeterinstitute.ca/mp3/1171ed57-abcb-4b31-b872-00c8b30af7b7.mp3 Science http://streamer.perimeterinstitute.ca/mp3/1171ed57-abcb-4b31-b872-00c8b30af7b7.mp3 Tue, 06 Dec 2005 16:00:31 -0500 A swashbuckling tale of greed, deception, and quantum data hiding on the high seas. When we hide or encrypt information, it's probably because that information is valuable. I present a novel approach to quantum data hiding based this assumption. An entangled treasure map marks the spot where a hoard of doubloons is buried, but the sailors sharing this map want all the treasure for themselves! How should they study their map using LOCC? This simple scenario yields a surprisingly rich and counterintuitive game theoretic structure. A maximally entangled map performs no better than a separable one, leaving the treasure completely exposed. But non-maximally entangled maps can hide the information almost perfectly. Warning: contains pirates. Jonathan Walgate http://streamer.perimeterinstitute.ca/mp3/3948eddb-368c-499c-9d6e-a69ff0449135.mp3 Science http://streamer.perimeterinstitute.ca/mp3/3948eddb-368c-499c-9d6e-a69ff0449135.mp3 Wed, 14 Dec 2005 16:00:00 -0500 We consider the problem of bounded-error quantum state identification: given one of two known states, what is the optimal probability with which we can identify the given state, subject to our guess being correct with high probability (but we are permitted to output "don't know" instead of a guess). We prove a direct product theorem for this problem. Our proof is based on semidefinite programming duality and the technique may be of wider interest. Using this result, we present two new exponential separations in the simultaneous message passing model of communication complexity. Both are shown in the strongest possible sense: -- we describe a relation that can be computed with O(log n) classical bits of communication in the presence of shared randomness, but needs n^(1/3) communication if the parties don't share randomness, even if communication is quantum; -- we describe a relation that can be computed with O(log n) classical bits of communication in the presence of shared entanglement, but needs (almost) n^(1/3) communication if the parties share randomness but no entanglement, even if communication is quantum. Dmitry Gavinsky http://streamer.perimeterinstitute.ca/mp3/54109b95-b815-4fab-af00-0b72d3ed6f97.mp3 Science http://streamer.perimeterinstitute.ca/mp3/54109b95-b815-4fab-af00-0b72d3ed6f97.mp3 Wed, 11 Jan 2006 16:00:27 -0500 The information spectrum approach gives general formulae for optimal rates of codes in many areas of information theory. In this talk I shall relate the information spectrum approach to Shannon information theory and explore its relationship to ``entropic'' properties including subadditivity, chain rules, Araki-Lieb inequlities, and monotonicity. Garry Bowen http://streamer.perimeterinstitute.ca/mp3/334ddef4-4a0f-4134-8903-f035cea629cc.mp3 Science http://streamer.perimeterinstitute.ca/mp3/334ddef4-4a0f-4134-8903-f035cea629cc.mp3 Wed, 25 Jan 2006 16:00:02 -0500 Asymptotic statements like the almost-equi-partition law, the theorm of Shannon Mc -Millan-Breiman, the theorem of Sanov have all natural quantum analogs. They all talk about the thermodynamik limit of quantum spin systems. I will try to summarize these results and sketch the main ideas of proof. Ruedi Seiler http://streamer.perimeterinstitute.ca/mp3/896c6283-d6c3-43f4-9a38-a34eec09d582.mp3 Science http://streamer.perimeterinstitute.ca/mp3/896c6283-d6c3-43f4-9a38-a34eec09d582.mp3 Wed, 08 Feb 2006 16:00:55 -0500 Quantum information methods have been recently used for studying the properties of ground state entanglement in several many body and field theory systems. We will discuss a thought experiment wherein entanglement can be extracted from the vacuum of a relativistic field theory into a pair of arbitrarily spatially separated atoms. In order to simulate the detection process, we will consider the ground state of a linear chain of cooled trapped ions, and discuss a scheme for detecting the entanglement between the ion's motional degrees of freedom. Alex Retzker http://streamer.perimeterinstitute.ca/mp3/ed2014c0-4420-40b6-94df-144c70d364b2.mp3 Science http://streamer.perimeterinstitute.ca/mp3/ed2014c0-4420-40b6-94df-144c70d364b2.mp3 Wed, 01 Mar 2006 16:00:18 -0500 The amount of nonlocality in the GHZ state can be quantified by determining how much classical communication is required to bring a local-hidden-variable model into agreement with the predictions of quantum mechanics. It turns out that one bit suffices, and, of course, nothing less will do. I will discuss generalizations of this result to graph states and its relation to the stabilizer formalism. Carlton Caves http://streamer.perimeterinstitute.ca/mp3/0322e707-f907-4368-bba3-5d8cc8a43468.mp3 Science http://streamer.perimeterinstitute.ca/mp3/0322e707-f907-4368-bba3-5d8cc8a43468.mp3 Wed, 08 Mar 2006 16:00:08 -0500 Scott Aaronson http://streamer.perimeterinstitute.ca/mp3/845a4b81-cee8-42f7-8481-a4de2f5b60a6.mp3 Science http://streamer.perimeterinstitute.ca/mp3/845a4b81-cee8-42f7-8481-a4de2f5b60a6.mp3 Wed, 15 Mar 2006 16:00:11 -0500 I will discuss a toy theory that reproduces a wide variety of qualitative features of quantum theory for degrees of freedom that are continuous. The ontology of the theory is that of classical particle mechanics, but it is assumed that there is a constraint on the amount of knowledge that an observer may have about the motional state of any collection of particles -- Liouville mechanics with an epistemic restriction. The formalism of the theory is determined by examining the consequences of this "classical uncertainty principle" on state preparations, measurements, and dynamics. The result is a theory of hidden variables, although it is not a hidden variable model of quantum theory because it is both local and noncontextual. Despite admitting a simple classical interpretation, the theory also exhibits the operational features of Bohr's notion of complementarity. In fact, it includes all of the features of quantum mechanics to which Bohr appeals in his response to EPR. This theory demonstrates, therefore, that Bohr's arguments fail as a defense of the completeness of quantum mechanics. Joint work with Stephen Bartlett and Terry Rudolph Robert Spekkens http://streamer.perimeterinstitute.ca/mp3/f6caaf77-3232-4a05-98a2-d1059255c9f7.mp3 Science http://streamer.perimeterinstitute.ca/mp3/f6caaf77-3232-4a05-98a2-d1059255c9f7.mp3 Wed, 22 Mar 2006 16:00:12 -0500 Alexei Grinbaum http://streamer.perimeterinstitute.ca/mp3/b0957630-07e4-45e2-8756-4cd3751c8173.mp3 Science http://streamer.perimeterinstitute.ca/mp3/b0957630-07e4-45e2-8756-4cd3751c8173.mp3 Wed, 29 Mar 2006 16:00:59 -0500 I will investigate the creation and detection of multipartite entangled states in systems of ultracold neutral atoms trapped in an optical lattice. These setups are scalable, highly versatile and controllable at the quantum level. Thus they provide an ideal test bed for studying the properties of multipartite entangled states. I will first present methods exploiting incoherent dynamics for initializing an atomic quantum register. The immersion of an optical lattice in a Bose-Einstein condensate leads to spontaneous emission of phonons. This process can be used for irreversibly loading and cooling atoms within the lowest Bloch band of the lattice. I will describe loading and cooling schemes based on this mechanism and compare them to conventional loading schemes. I will then show how coherent dynamics in a very strongly interacting 1D optical lattice setup can be used for the efficient generation of arbitrary graph states in the atomic quantum register. This system can be mapped onto an XY spin chain which itself is equivalent to a system of non-interacting fermions. By exploiting the anticommutation relations between these fictitious fermions I will discuss how any graph state can be realized in an efficient and robust way. In the final part of my talk I will present a practical method for detecting and characterizing multipartite entangled states in atomic quantum registers. This scheme is based on measuring violations of entropic inequalities using simple quantum networks involving only two copies of the quantum state under consideration. I will investigate the performance of this method under realistic conditions taking into account the most common sources of experimental errors. Dieter Jaksch http://streamer.perimeterinstitute.ca/mp3/7f68d869-a25c-481b-a877-39efff9d8f25.mp3 Science http://streamer.perimeterinstitute.ca/mp3/7f68d869-a25c-481b-a877-39efff9d8f25.mp3 Wed, 05 Apr 2006 16:00:23 -0400 Hamiltonian oracles are the continuum limit of the standard unitary quantum oracles. In addition to being a potentially useful tool in the study of standard oracles, Hamiltonian oracles naturally introduce the concept of fractional queries and are amenable to study using techniques of differential equations and geometry. As an example of these ideas we shall examine the Hamiltonian oracle corresponding to the problem of oracle interrogation. This talk is intended for all those who wish to apply their knowledge of differential geometry without the risk of creating an event horizon. Carlos Mochon http://streamer.perimeterinstitute.ca/mp3/14089026-3c4b-46b0-8941-a9c5c83e9866.mp3 Science http://streamer.perimeterinstitute.ca/mp3/14089026-3c4b-46b0-8941-a9c5c83e9866.mp3 Wed, 19 Apr 2006 16:00:31 -0400 While modern theories lavishly invoke several spatial dimensions within models that seek to unify relativity theory and quantum mechanics, none seems to consider the possibility that a yet-unfamiliar aspect of time may do the work. I introduce the notion of Becoming and then consider its consequences for physical theory. Becoming portrays a possible aspect of time that is "curled" very much like the extra spatial dimensions in superstring theories. Within the resulting picture of spacetime, some fundamental aspects of quantum mechanics, special and general relativity, thermodynamics and modern cosmology fit in very naturally. The proposed model is not yet a scientific theory as it still lacks a rigorous formalism and experimental predictions, yet it points out an entire family of possible theories that merit serious consideration. Avshalom Elitzur http://streamer.perimeterinstitute.ca/mp3/0ecdfe98-46d9-466c-973d-1fbec948ec3c.mp3 Science http://streamer.perimeterinstitute.ca/mp3/0ecdfe98-46d9-466c-973d-1fbec948ec3c.mp3 Fri, 21 Apr 2006 10:00:13 -0400 Entanglement entropy is currently of interest in several areas in physics, such as condensed matter, field theory, and quantum information. One of the most interesting properties of the entanglement entropy is its scaling behavior, especially close to phase transitions. It was believed that for dimensions higher than 1 the entropy scales like surface area of the subsystem. We will describe a recent result for free fermions at zero temperature, where the entropy in fact scales faster. The latter problem will be related to a mathematical conjecture due to H. Widom (1982). This is a joint work with I. Klich. Dimitri Gioev http://streamer.perimeterinstitute.ca/mp3/d2e3ac31-d94e-466b-976b-b08ddffa5e3e.mp3 Science http://streamer.perimeterinstitute.ca/mp3/d2e3ac31-d94e-466b-976b-b08ddffa5e3e.mp3 Wed, 26 Apr 2006 16:00:14 -0400 Inspired by the notion that the differences between quantum theory and classical physics are best expressed in terms of information theory, Hardy (2001) and Clifton, Bub, and Halvorson (2003) have constructed frameworks general enough to embrace both quantum and classical physics, within which one can invoke principles that distinguish the classical from the quantum. Independently of any view that quantum theory is essentially about quantum information, such frameworks provide a useful tool for exploring the differences between classical and quantum physics, and the relations between the various properties of quantum mechanics that distinguish it from the classical. In particular, we can ask: on which features of quantum physics do our familiar possibility/impossibility theorems depend? It turns out that it is possible to extend the no-cloning theorem and other results, such as the Holevo bound on acquisition of information by a single measurement, beyond the quantum setting. Wayne Myrvold http://streamer.perimeterinstitute.ca/mp3/f73324ab-59d4-4e3f-a7db-edb76bd76830.mp3 Science http://streamer.perimeterinstitute.ca/mp3/f73324ab-59d4-4e3f-a7db-edb76bd76830.mp3 Wed, 03 May 2006 16:00:15 -0400 We will look at the axioms of quantum mechanics as expressed, for example, in the book by M. A. Nielsen and I. L. Chung ("Quantum Computation and Quantum Information"). We then take a critical look at these axioms, raising several questions as we go. In particular, we will look at the possible informational completeness property of the family of operators that we measure. We will propose physical solutions based on the results of quantum mechanics on phase space and the measurement of quantum particles by quantum mechanical means. We illustrate this with both momentum-position measurements and spin measurements. Franklin Schroeck http://streamer.perimeterinstitute.ca/mp3/2316a6d4-1f4e-4305-b2d5-9f15e7fc50bb.mp3 Science http://streamer.perimeterinstitute.ca/mp3/2316a6d4-1f4e-4305-b2d5-9f15e7fc50bb.mp3 Wed, 10 May 2006 16:00:26 -0400 This talk is concerned with the noise-insensitive transmission of quantum information. For this purpose, the sender incorporates redundancy by mapping a given initial quantum state to a messenger state on a larger-dimensional Hilbert space. This encoding scheme allows the receiver to recover part of the initial information if the messenger system is corrupted by interaction with its environment. Our noise model for the transmission leaves a part of the quantum information unchanged, that is, we assume the presence of a noiseless subsystem or of a decoherence-free subspace. We address the case when the noiseless component cannot contain all the quantum information to be transmitted, and investigate how to best spread the information in a quantum state across the noise-susceptible components. (Joint work with David Kribs and Vern Paulsen.) Bernhard Bodmann http://streamer.perimeterinstitute.ca/mp3/5c759361-1801-48bc-8b86-4aa5926c8e36.mp3 Science http://streamer.perimeterinstitute.ca/mp3/5c759361-1801-48bc-8b86-4aa5926c8e36.mp3 Wed, 17 May 2006 16:00:54 -0400 It is somewhat surprising, but problems in quantum computing lead to problems in algebraic graph theory. I will discuss some instances that I am familiar with, and note a commmon thread. Chris Godsil http://streamer.perimeterinstitute.ca/mp3/ba6e586f-8c19-4fa0-b9f2-d14aeab5a46b.mp3 Science http://streamer.perimeterinstitute.ca/mp3/ba6e586f-8c19-4fa0-b9f2-d14aeab5a46b.mp3 Wed, 24 May 2006 16:00:48 -0400 Clifton, Bub, and Halvorson claim to be able to derive quantum mechanics from information-theoretic axioms. However, their derivation relies on the auxiliary assumption that the relevant probabilities for measurement outcomes can be represented by the observables (self-adjoint operators) and states of a C*-algebra. There are legitimate probability theories that are not so representable --- in particular, the nonlocal boxes of Popescu and Rohrlich. We explain the impact of nonlocal boxes on the interpretation of the CBH derivation, and we discuss possible generalizations of the CBH derivation in the framework of these more general probability theories. Hans Halvorson http://streamer.perimeterinstitute.ca/mp3/9da12bba-deab-4728-809b-b4e873541b84.mp3 Science http://streamer.perimeterinstitute.ca/mp3/9da12bba-deab-4728-809b-b4e873541b84.mp3 Mon, 29 May 2006 14:30:55 -0400 Adiabatic Quantum Computation is not only a possibly more robust alternative to standard quantum computation. Since it considers a continuous-time evolution of the system, it also provides a natural bridge towards studying the dynamics of interacting many-particle quantum systems, quantum phase transitions and other issues in fundamental physics. After a brief review of adiabatic quantum computation, I will show our recent results on the dynamics of entanglement and fidelity for the search and Deutsch algorithms including several variations and optimization. I will show how these studies led to suggesting an alternative definition of entanglement and compare the results, and discuss possible implications for considering entanglement a resource. I will conclude with an outlook on further applications and extensions of adiabatic quantum computation. Daria Ahrensmeier http://streamer.perimeterinstitute.ca/mp3/efd1e7d2-6c6e-4622-887b-a8623ed9c092.mp3 Science http://streamer.perimeterinstitute.ca/mp3/efd1e7d2-6c6e-4622-887b-a8623ed9c092.mp3 Wed, 07 Jun 2006 16:00:29 -0400 The modern view of representing a quantum observable as a semispectral measure as opposed to the traditional approach of using only spectral measures has added a great deal to our understanding of the mathematical structures and conceptual foundations of quantum mechanics. The old questions of 1) how to determine a quantum observable from its classical counter-part (if any), 2) how much statistical information is needed to determine an observable, 3) which observables can be measured together, and 4) are there noiseless measurements, all appear in a new perspective, calling for a study of problems such as: 1) how to obtain a semispectral measure by a quantization map, 2) do the moment operators of a semispectral measure determine the operator measure, 3) are coexistent observables jointly measurable, and 4) does minimal variance occur only in the case of a spectral measure? In my talk I will survey some of the recent developments concerning these questions and problems. Pekka Lahti http://streamer.perimeterinstitute.ca/mp3/3287359c-9197-4232-802e-dd2e38ea0463.mp3 Science http://streamer.perimeterinstitute.ca/mp3/3287359c-9197-4232-802e-dd2e38ea0463.mp3 Wed, 14 Jun 2006 16:00:21 -0400 In this talk, I will outline a quantum generalization of causal networks that are used to analyze complex probabilistic inference problems involving large numbers of correlated random variables. I will review the framework of classical causal networks and the graph theoretical constructions that are abstracted from them, including entailed conditional independence, d-separation and Markov equivalence. I will show how to generalize the definition of causal networks to the quantum case, such that the same graph theoretic constructions apply, and give an explicit representation of the states supported on the graph as the Gibbs states of certain classes of Hamiltonians. Matthew Leifer http://streamer.perimeterinstitute.ca/mp3/0506921c-e760-42d2-94e5-343f5a5cf131.mp3 Science http://streamer.perimeterinstitute.ca/mp3/0506921c-e760-42d2-94e5-343f5a5cf131.mp3 Wed, 28 Jun 2006 16:00:18 -0400 In order to predict the future state of a quantum system, we generally do not need to know the past state of the entire universe, but only the state of a finite neighborhood of the system. This locality is best expressed as a restriction on how information "flows" between systems. In this talk I will describe some recent work, inspired by quantum cellular automata, about the information strucutre of local quantum dynamics. Issues to be discussed include the definition of "locality", some characterization theorems, connections between classical and quantum locality for reversible maps, the relation between local and global dynamics, and the dissection of CNOT. Ben Schumacher http://streamer.perimeterinstitute.ca/mp3/27bdb7ed-198d-4a44-b969-fef69a413cfa.mp3 Science http://streamer.perimeterinstitute.ca/mp3/27bdb7ed-198d-4a44-b969-fef69a413cfa.mp3 Wed, 05 Jul 2006 16:00:12 -0400 In this talk I will present several new results from joint work with Dmitry Gavinsky, Oded Regev and Ronald de Wolf, relating to the model of one-way communication and the simultaneous model of communication. I will describe several separations between various resources (entanglement versus event coin, quantum communication versus classical communication), showing in particular that quantum communication cannot simulate a public coin and that entanglement can be much more powerful than a public coin, even if communication is quantum. I will also present a characterization of the quantum fingerprinting technique. Julia Kempe http://streamer.perimeterinstitute.ca/mp3/8a1a4b74-21d5-4106-89e5-0aeed4dc15c8.mp3 Science http://streamer.perimeterinstitute.ca/mp3/8a1a4b74-21d5-4106-89e5-0aeed4dc15c8.mp3 Wed, 30 Aug 2006 16:00:00 -0400 My field is the foundations of quantum mechanics, in particular Bohmian mechanics, a non-relativistic theory that is empirically equivalent to standard quantum mechanics while solving all of its paradoxes in an elegant and simple way, essentially by assuming that particles have trajectories. Bohmian mechanics possesses a straightforward generalization to relativistic space-time, be it flat or curved, if one assumption against the spirit of relativity is granted: the existence of a "time foliation", i.e., a physical object mathematically represented by a slicing of space-time into spacelike 3-surfaces, which evolves according to a Lorentz-invariant law. On the basis of this kind of theory, describing particles in a background 4-geometry, I propose an extension in which the space-time geometry is dynamically generated, as in general relativity. Whether my model is empirically equivalent to any known type of quantum gravity I don't know. In this model, there is a Lorentzian metric on configuration-space-time, evolving according to the higher-dimensional analog of the Einstein field equation. The 4-metric is obtained from the configuration-space-time metric and the actual particle configuration. Thus, this Bohm-like model generates (up to diffeomorphisms) a 4-metric and particle world lines from a given wave function. Roderich Tumulka http://streamer.perimeterinstitute.ca/mp3/61fa8a3e-b966-41fe-addb-e20a00af533a.mp3 Science http://streamer.perimeterinstitute.ca/mp3/61fa8a3e-b966-41fe-addb-e20a00af533a.mp3 Tue, 19 Sep 2006 04:00:00 -0400 Entanglement is one of the most studied features of quantum mechanics and in particular quantum information. Yet its role in quantum information is still not clearly understood. Results such as (R. Josza and N. Linden, Proc. Roy. Soc. Lond. A 459, 2011 (2003)) show that entanglement is necessary, but stabilizer states and the Gottesman-Knill theorem (for example) imply that it is far from sufficient. I will discuss three aspects of entanglement. First, a quantum circuit with a "vanishingly small" amount of entanglement that admits an apparent exponential speed-up over the classical case. Second, I will discuss techniques for lower-bounding the amount of entanglement in bipartite quantum states. Finally, I will discuss the role of entanglement in quantum metrology. Specifically, I will show that entangling ancillas can make no difference to the accuracy of a quantum parameter estimation, regardless of the nature of the coupling Hamiltonian. I will conclude by discussing strategies for improving the scaling of quantum parameter estimation. Steve Flammia http://streamer.perimeterinstitute.ca/mp3/08a3e08f-4b21-48b9-8908-3ca1472d8bd1.mp3 Science http://streamer.perimeterinstitute.ca/mp3/08a3e08f-4b21-48b9-8908-3ca1472d8bd1.mp3 Thu, 21 Sep 2006 16:00:00 -0400 Quantum mechanics is a non-classical probability calculus -- but hardly the most general one imaginable. In this talk, I'll discuss some familiar non-classical properties of quantum-probabilistic models that turn out to be features of {em all} non-classical models. These include a generic no-cloning theorem obtained in recent work with Howard Barnum, Jon Barrett and Matt Leifer. Alexander Wilce http://streamer.perimeterinstitute.ca/mp3/5cec474c-9cb3-4fbe-8542-41b0e82b847d.mp3 Science http://streamer.perimeterinstitute.ca/mp3/5cec474c-9cb3-4fbe-8542-41b0e82b847d.mp3 Fri, 22 Sep 2006 15:00:00 -0400 We describe a protocol for distilling maximally entangled bipartite states between random pairs of parties (``random entanglement'') from those sharing a tripartite W state, and show that this may be done at a higher rate than distillation of bipartite entanglement between specified pairs of parties (``specified entanglement''). Specifically, the optimal distillation rate for specified entanglement for the W has been previously shown to be the asymptotic entanglement of assistance of 0.92 EPR pairs per W, while our protocol can distill 1 EPR pair per W between random pairs of parties, which we conjecture to be optimal. We further extend this to a more general class of W-like states and show by increasing the number of parties in the protocol that there exist states with fixed lower-bounded distillable random entanglement for arbitrarily small specified entanglement. [Work done in collaboration with Benjamin Fortescue. Preprint available at http://arxiv.org/abs/quant-ph/0607126 ] Hoi-Kwong Lo http://streamer.perimeterinstitute.ca/mp3/cf538d5c-47d2-4305-b0e4-d8ed51b892ca.mp3 Science http://streamer.perimeterinstitute.ca/mp3/cf538d5c-47d2-4305-b0e4-d8ed51b892ca.mp3 Mon, 25 Sep 2006 16:00:00 -0400 TBA Itamar Pitowsky http://streamer.perimeterinstitute.ca/mp3/022564b9-17b1-439e-b5e9-7b24d2928d59.mp3 Science http://streamer.perimeterinstitute.ca/mp3/022564b9-17b1-439e-b5e9-7b24d2928d59.mp3 Tue, 03 Oct 2006 09:00:00 -0400 TBA Dorit Aharonov http://streamer.perimeterinstitute.ca/mp3/bd491b81-256f-47f0-a7fa-747ac769f597.mp3 Science http://streamer.perimeterinstitute.ca/mp3/bd491b81-256f-47f0-a7fa-747ac769f597.mp3 Wed, 11 Oct 2006 04:00:00 -0400 I will discuss various different ways of quantifying the differences between two quantum observables (POVMs). Each of these approaches gives rise to a notion of approximately measuring one observable by means of measuring some other observable. This will be illustrated in the case of position and momentum by studying the question which POVMs on phase space can reasonably be said to represent a joint approximate determination of these observables. A new, universally valid trade-off relation for the associated inaccuracies will be rigorously formulated. I will sketch the proof which is an adaptation of some interesting techniques and properties of covariant phase space observables used recently by R Werner in a related project. Recommended reading (optional): quant-ph/0405184 (R Werner), quant-ph/0609185 (PB et al), and also for further background information quant-ph/0309091 (M Hall), quant-ph/0310070 (M Ozawa), quant-ph/9803051 (DM Appleby). Paul Busch http://streamer.perimeterinstitute.ca/mp3/0c6669ce-5baa-4331-ac35-8ec603a646c5.mp3 Science http://streamer.perimeterinstitute.ca/mp3/0c6669ce-5baa-4331-ac35-8ec603a646c5.mp3 Wed, 18 Oct 2006 16:00:00 -0400 Complexity class MA is a class of yes/no problems for which the answer `yes' has a short certificate that can be efficiently checked by a classical randomized algorithm. We prove that MA has a natural complete problem: stoquastic k-SAT. This is a quantum-mechanical analogue of the satisfiability problem such that k-bit clauses are replaced by k-qubit projectors with non-negative matrix elements. Complexity class AM is a generalization of MA in which the certificate may include a short conversation between Prover and Verifier. We prove that AM also has a natural complete problem: stoquastic Local Hamiltonian with a quenched disorder. The problem is to evaluate expectation value of the ground state energy of disordered local Hamiltonian with non-positive matrix elements. Sergey Bravyi http://streamer.perimeterinstitute.ca/mp3/dc04b230-ae18-4574-b7fe-70bd7cb6f971.mp3 Science http://streamer.perimeterinstitute.ca/mp3/dc04b230-ae18-4574-b7fe-70bd7cb6f971.mp3 Wed, 08 Nov 2006 16:00:00 -0500 In this talk, I will show how to efficiently generate graph states based on realistic linear optics (with imperfect photon detectors and source), how to do scalable quantum computation with probabilistic atom photon interactions, and how to simulate strongly correlated many-body physics with ultracold atomic gas. Luming Duan http://streamer.perimeterinstitute.ca/mp3/27393a94-b535-417b-9b7d-8a372edfa8a3.mp3 Science http://streamer.perimeterinstitute.ca/mp3/27393a94-b535-417b-9b7d-8a372edfa8a3.mp3 Wed, 15 Nov 2006 16:00:00 -0500 Most modern discussions of Bell's theorem take microscopic causality (the arrow of time) for granted, and raise serious doubts concerning realism and/or relativity. Alternatively, one may allow a weak form of backwards-in-time causation, by considering "causes" to have not only "effects" at later times but also "influences" at earlier times. These "influences" generate the correlations of quantum entanglement, but do not enable information to be transmitted to the past. Can one realize this scenario in a mathematical model? If macroscopic time-asymmetry is introduced by imposing initial conditions, such a model can not be deterministic. Stochastic Quantization (Parisi and Wu,1981) is a non-deterministic approach known to reproduce quantum field theory. Based on this, a search for models displaying quantum nonlocal correlations, while maintaining the principles of realism, relativity and macroscopic causality, is proposed. Nathan Argaman http://streamer.perimeterinstitute.ca/mp3/901ee082-00f1-47bf-8986-c647ab98377e.mp3 Science http://streamer.perimeterinstitute.ca/mp3/901ee082-00f1-47bf-8986-c647ab98377e.mp3 Wed, 22 Nov 2006 04:00:00 -0500 We explore the role of rotational symmetry of quantum key distribution (QKD) protocols in their security. Specifically, in the first part of the talk, we consider a generalized QKD protocol with discrete rotational symmetry. Note that, before our work, each QKD protocol seems to have a different security proof. Given that the techniques of those proofs are similar, it will be interesting to have a unified proof for QKD protocols with symmetry (e.g., the BB84 protocol and the SARG04 protocol). This is exactly what we achieve in our work. We show that rotational symmetry plays an important role in the unified security proof of QKD protocols with symmetry, leading to simple and structural security relations. In the second part, we consider a QKD protocol that does not possess rotational symmetry and analyze its security. Interestingly, even without any rotational symmetry, this protocol can still be proven secure. However, the security relation is not as simple as those in the first part, due to the lack of symmetry. Therefore, although rotational symmetry is not required in a QKD protocol to ensure its security, rotational symmetry does provide significant simplification in the security analysis, leading to simple security relations. Fred Fung http://streamer.perimeterinstitute.ca/mp3/f1110ee2-406a-46af-be6e-cf41746a54e6.mp3 Science http://streamer.perimeterinstitute.ca/mp3/f1110ee2-406a-46af-be6e-cf41746a54e6.mp3 Wed, 29 Nov 2006 16:00:00 -0500 Although entanglement constitutes one of the most remarkable differences between classical and quantum mechanics, and entanglement does have directly observable consequences, entanglement is not a regular observable like momentum or energy. It is rather a non-linear functional of a typically large set of such observables. Therefore, one often needs to perform many different measurements, in order to determine the degree of entanglement of a given quantum state. We show, how the number of measurement can be reduced -- sometimes to a single one -- if collective observables are measured, that respect the natural invariance properties of entangled states. Finally, we discuss the implementation of this approach in a laboratory experiment. Nature 440, 1022 (2006) PRL 79, 050501 (2006) quant-ph/0605250 Florian Mintert http://streamer.perimeterinstitute.ca/mp3/0e201666-c181-4406-a4ba-7693e23fc8ad.mp3 Science http://streamer.perimeterinstitute.ca/mp3/0e201666-c181-4406-a4ba-7693e23fc8ad.mp3 Wed, 06 Dec 2006 16:30:00 -0500 Yi Zhao http://streamer.perimeterinstitute.ca/mp3/d35f05d8-aace-4836-a7b6-5cf2b43ccd0c.mp3 Science http://streamer.perimeterinstitute.ca/mp3/d35f05d8-aace-4836-a7b6-5cf2b43ccd0c.mp3 Wed, 13 Dec 2006 16:00:00 -0500 Kolmogorov complexity is a measure of the information contained in a binary string. We investigate the notion of quantum Kolmogorov complexity, a measure of the information required to describe a quantum state. We show that for any definition of quantum Kolmogorov complexity measuring the number of classical bits required to describe a pure quantum state, there exists a pure n-qubit state which requires exponentially many bits of description. This is shown by relating the classical communication complexity to the quantum Kolmogorov complexity. Furthermore we give some examples of how quantum Kolmogorov complexity can be applied to prove results in different fields, such as quantum computation and communication. Caterina-Eloisa Mora http://streamer.perimeterinstitute.ca/mp3/b4fa9815-d76c-4281-b617-f0c43853bd61.mp3 Science http://streamer.perimeterinstitute.ca/mp3/b4fa9815-d76c-4281-b617-f0c43853bd61.mp3 Wed, 10 Jan 2007 16:00:00 -0500 A multi-partite entanglement measure is constructed via the distance or angle of the pure state to its nearest unentangled state. The extention to mixed states is made via the convex-hull construction, as is done in the case of entanglement of formation. This geometric measure is shown to be a monotone. It can be calculated for various states, including arbitrary two-qubit states, generalized Werner and isotropic states in bi-partite systems. It is also calculated for various multi-partite pure and mixed states, including ground states of some physical models and states generated from quantum alogrithms, such as Grover's. A specific application to a spin model with quantum phase transistions will be presented in detail.The connection of the geometric measure to other entanglement properties will also be discussed. Tzu-Chieh Wei http://streamer.perimeterinstitute.ca/mp3/4cf69fd0-51da-4cae-a14e-c263a2a574cf.mp3 Science http://streamer.perimeterinstitute.ca/mp3/4cf69fd0-51da-4cae-a14e-c263a2a574cf.mp3 Wed, 17 Jan 2007 16:00:00 -0500 If a large quantum computer (QC) existed today, what type of physical problems could we efficiently simulate on it that we could not simulate on a conventional computer? In this talk, I argue that a QC could solve some relevant physical "questions" more efficiently. First, I will focus on the quantum simulation of quantum systems satisfying different particle statistics (e.g., anyons), using a QC made of two-level physical systems or qubits. The existence of one-to-one mappings between different algebras of observables or between different Hilbert spaces allow us to represent and imitate any physical system by any other one (e.g., a bosonic system by a spin-1/2 system). We explain how these mappings can be performed showing quantum networks useful for the efficient evaluation of some physical properties, such as correlation functions and energy spectra. Second, I will focus on the quantum simulation of classical systems. Interestingly, the thermodynamic properties of any d-dimensional classical system can be obtained by studying the zero-temperature properties of an associated d-dimensional quantum system. This classical-quantum correspondence allows us to understand classical annealing procedures as slow (adiabatic) evolutions of the lowest-energy state of the corresponding quantum system. Since many of these problems are NP-hard and therefore difficult to solve, is worth investigating if a QC would be a better device to find the corresponding solutions. Rolando Somma http://streamer.perimeterinstitute.ca/mp3/1d92605f-eb9b-43c3-a253-42c8bb9c0f42.mp3 Science http://streamer.perimeterinstitute.ca/mp3/1d92605f-eb9b-43c3-a253-42c8bb9c0f42.mp3 Mon, 22 Jan 2007 16:00:00 -0500 We propose an extended quantum theory, in which the number of degrees of freedom K behaves as FOURTH power the number N of distinguishable states. As the simplex of classical N--point probability distributions can be embedded inside a higher dimensional convex body of mixed quantum states, one can further increase the dimensionality constructing the set of extended quantum states. The embedding proposed corresponds to an assumption that the physical system described in N dimensional Hilbert space is coupled with an auxiliary subsystem of the same dimensionality. The extended theory is shown to be a non-trivial generalisation of the standard quantum theory for which K=N^2. Imposing certain restrictions on initial conditions and dynamics allowed in the quartic theory one obtains quadratic theory as a special case. We discuss the question, how the theory of information processing looks like in the framework of the generalised quantum theory. In particular we propose a scheme of extended dense coding, in which one transmits two qubits by sending one extended bit, provided it was initially entangled with the extended bit of the receiver. Karol Zyczkowski http://streamer.perimeterinstitute.ca/mp3/cee1c425-8428-4512-a62e-481f930377b7.mp3 Science http://streamer.perimeterinstitute.ca/mp3/cee1c425-8428-4512-a62e-481f930377b7.mp3 Wed, 21 Feb 2007 16:00:00 -0500 We show that singlets composed of multiple multi-level quantum systems can naturally arise as the ground state of a physically-motivated Hamiltonian. The Hamiltonian needs to be one which simply exchanges the states of nearest neighbours in any graph of interacting d-level quantum systems (qudits) as long as the graph also has d sites. We point out that local measurements on some of these qudits, with the freedom of choosing a distinct measurement basis at each qudit randomly from an infinite set of bases, project the remainder onto a singlet state. One implication of this is that the entanglement in these states is very robust (persistent), while an application is in establishing an arbitrary amount of entanglement between well-separated parties (for subsequent use as a communication resource) by local measurements on an appropriate graph. Based on quant-ph/0602139. Christopher Hadley http://streamer.perimeterinstitute.ca/mp3/85da255f-581a-4165-8301-6846d7bf9c6a.mp3 Science http://streamer.perimeterinstitute.ca/mp3/85da255f-581a-4165-8301-6846d7bf9c6a.mp3 Wed, 07 Mar 2007 16:00:00 -0500 We give a communication problem between two players, Alice and Bob, that can be solved by Alice sending a quantum message to Bob, for which any classical interactive protocol requires exponentially more communication. Dmitry Gavinsky http://streamer.perimeterinstitute.ca/mp3/593ef9f3-f2d8-466f-9ef6-79e01ca98a45.mp3 Science http://streamer.perimeterinstitute.ca/mp3/593ef9f3-f2d8-466f-9ef6-79e01ca98a45.mp3 Wed, 21 Mar 2007 16:00:00 -0400 Consider a discrete quantum system with a d-dimensional state space. For certain values of d, there is an elegant information-theoretic uncertainty principle expressing the limitation on one's ability to simultaneously predict the outcome of each of d+1 mutually unbiased--or mutually conjugate--orthogonal measurements. (The allowed values of d include all powers of primes, and at present it is not known whether any value of d is excluded.) In this talk I show how states that minimize uncertainty in this sense can be generated via a discrete phase space based on finite fields. I also discuss some numerically observed features of these minimum-uncertainty states as the dimension d gets very large. William Wootters http://streamer.perimeterinstitute.ca/mp3/b5a7ccf0-c2f7-4b10-981e-3e9694b077e2.mp3 Science http://streamer.perimeterinstitute.ca/mp3/b5a7ccf0-c2f7-4b10-981e-3e9694b077e2.mp3 Wed, 28 Mar 2007 16:00:00 -0400 After a brief overview of the three broad classes of superconducting quantum bits (qubits)--flux, charge and phase--I describe experiments on single and coupled flux qubits. The quantum state of a flux qubit is measured with a Superconducting QUantum Interference Device (SQUID). Single flux qubits exhibit the properties of a spin-1/2 system, including superposition of quantum states, Rabi oscillations and spin echoes. Two qubits, coupled by their mutual inductance and by screening currents in the readout SQUID, produce a ground state |0> and three excited states |1>, |2> and |3>. Microwave spectra reveal an anticrossing between the |1>and |2> energy levels. The level repulsion can be reduced to zero by means of a current pulse in the SQUID that changes its dynamic inductance and hence the coupling between the qubits. The results are in good agreement with predictions. The ability to switch the coupling between qubits on and off permits efficient realization of universal quantum logic. This work was in collaboration with T. Hime, B.L.T. Plourde, P.A. Reichardt, T.L. Robertson, A. Ustinov, K.B. Whaley, F.K. Wilhelm and C.-E. Wu, and supported by AFOSR, ARO and NSF. John Clarke http://streamer.perimeterinstitute.ca/mp3/35e95108-06f9-46af-9bfc-c71163234ade.mp3 Science http://streamer.perimeterinstitute.ca/mp3/35e95108-06f9-46af-9bfc-c71163234ade.mp3 Wed, 04 Apr 2007 16:00:00 -0400 Inelastic collisions occur in Bose-Einstein condensates, in some cases, producing particle loss in the system. Nevertheless, these processes have not been studied in the case when particles do not escape the trap. We show that such inelastic processes are relevant in quantum properties of the system such as the evolution of the relative population and entanglement. Moreover, including inelastic terms in the models of multimode condensates allows for an exact analytical solution.  Ivette Fuentes http://streamer.perimeterinstitute.ca/mp3/b37fac60-affd-4696-b0bd-0ed24a006e24.mp3 Science http://streamer.perimeterinstitute.ca/mp3/b37fac60-affd-4696-b0bd-0ed24a006e24.mp3 Wed, 11 Apr 2007 16:00:00 -0400 I will survey recent feasibility results on building multi-party cryptographic protocols which manipulate quantum data or are secure against quantum adversaries. The focus will be protocols for secure evaluation of quantum circuits. Along the way, I'll discuss how quantum machines can (and can't) prove knowledge of a secret to a distrustful partner. The talk is based on recent unpublished results, as well as older joint work with subsets of Michael Ben-Or, Claude Crepeau, Daniel Gottesman, and Avinatan Hasidim (STOC '02, FOCS '02, Eurocrypt '05, FOCS '06). Adam Brown http://streamer.perimeterinstitute.ca/mp3/c1fe643c-2582-4e6a-9af9-b689bbf8318f.mp3 Science http://streamer.perimeterinstitute.ca/mp3/c1fe643c-2582-4e6a-9af9-b689bbf8318f.mp3 Wed, 25 Apr 2007 16:00:00 -0400 In nearly every quantum algorithm which exponentially outperforms the best classical algorithm the quantum Fourier transform plays a central role. Recently, however, cracks in the quantum Fourier transform paradigm have begun to emerge. In this talk I will discuss one such development which arises in a new efficient quantum algorithm for the Heisenberg hidden subgroup problem. In particular I will show how considerations of symmetry for this hidden subgroup problem lead naturally to a different transform than the quantum Fourier transform, the Clebsch-Gordan transform over the Heisenberg group. Clebsch-Gordan transforms over finite groups thus appear to be an important new tool for those attempting to find new quantum algorithms. [Part of this work was done in collaboration with Andrew Childs (Caltech) and Wim van Dam (UCSB)] Dave Bacon http://streamer.perimeterinstitute.ca/mp3/d063dc80-9290-44be-8f8e-902fc95c8d61.mp3 Science http://streamer.perimeterinstitute.ca/mp3/d063dc80-9290-44be-8f8e-902fc95c8d61.mp3 Wed, 16 May 2007 16:00:00 -0400 In this talk we discuss how large classes of classical spin models, such as the Ising and Potts models on arbitrary lattices, can be mapped to the graph state formalism. In particular, we show how the partition function of a spin model can be written as the overlap between a graph state and a complete product state. Here the graph state encodes the interaction pattern of the spin model---i.e., the lattice on which the model is defined---whereas the product state depends only on the couplings of the model, i.e., the interaction strengths. As main examples, we find that the 1D Ising model corresponds to the 1D cluster state, the 2D Ising model without external field is mapped to Kitaev's toric code state, and the 2D Ising model with external field corresponds to the 2D cluster state---but the mappings are completely general in that arbitrary graphs, and also q-state models can be treated. These mappings allow one to make connections between concepts in (classical) statistical mechanics and quantum information theory and to obtain a cross-fertilization between both fields. As a main application, we will prove that the classical Ising model on a 2D square lattice (with external field) is a "complete model", in the sense that the partition function of any other spin model---i.e., for q-state spins on arbitrary lattices---can be obtained as a special instance of the (q=2) 2D Ising partition function with suitably tuned (complex) couplings. This result is obtained by invoking the above mappings from spin models to graph states, and the property that the 2D cluster states are universal resource states for one-way quantum computation. Joint work with Wolfgang Duer and Hans Briegel, see PRL/ 98 117207 (2007)/ and quant-ph/0708.2275. For related work, see also S. Bravyi and R. Raussendorf, quant-ph/0610162. Maarten Van den Nest http://streamer.perimeterinstitute.ca/mp3/e4dc9f56-22a9-4542-af57-8bc6fb2e2026.mp3 Science http://streamer.perimeterinstitute.ca/mp3/e4dc9f56-22a9-4542-af57-8bc6fb2e2026.mp3 Wed, 12 Sep 2007 16:00:00 -0400 It is known that finite fields with d elements exist only when d is a prime or a prime power. When the dimension d of a finite dimensional Hilbert space is a prime power, we can associate to each basis state of the Hilbert space an element of a finite or Galois field, and construct a finite group of unitary transformations, the generalised Pauli group or discrete Heisenberg-Weyl group. Its elements can be expressed, in terms of the elements of a Galois field. This group presents numerous applications in Quantum Information Science e.g. tomography, dense coding, teleportation, error correction and so on. The aim of our talk is to give a general survey of these properties and to present recently obtained results in connection with three problems: -the so-called ''Mean King's problem'' in prime power dimension, -discrete Wigner distributions, -and quantum tomography . Finally we shall discuss a limitation of the possible dimensions in which the so-called epistemic interpretation can be consistently formulated, in relation with the existence of finite affine planes, Euler's conjecture and the 36 officers problem. Thomas Durt http://streamer.perimeterinstitute.ca/mp3/ab38d6dd-dca1-4062-ab9a-c1c0994a3a53.mp3 Science http://streamer.perimeterinstitute.ca/mp3/ab38d6dd-dca1-4062-ab9a-c1c0994a3a53.mp3 Wed, 10 Oct 2007 16:00:00 -0400 Entanglement plays a fundamental role in quantum information processing and is regarded as a valuable, fungible resource, The practical ability to transform (or manipulate) entanglement from one form to another is useful for many applications. Usually one considers entanglement manipulation of states which are multiple copies of a given bipartite entangled state and requires that the fidelity of the transformation to (or from) multiple copies of a maximally entangled state approaches unity asymptotically in the number of copies of the original state. The optimal rates of these protocols yield two asymptotic measures of entanglement, namely, entanglement cost and distillable entanglement. It is not always justified, however, to assume that the entanglement resource available, consists of states which are multiple copies, i.e.,tensor products, of a given entangled state. More generally, an entanglement resource is characterized by an arbitrary sequence of bipartite states which are not necessarily of the tensor product form. In this seminar, we address the issue of entanglement manipulation for such general resources and obtain expressions for the entanglement cost and distillable entanglement. Nilanjana Datta http://streamer.perimeterinstitute.ca/mp3/19cb4af1-3bb3-45f1-8c71-f531b43ea690.mp3 Science http://streamer.perimeterinstitute.ca/mp3/19cb4af1-3bb3-45f1-8c71-f531b43ea690.mp3 Wed, 17 Oct 2007 16:00:00 -0400 We give a convenient representation for any map which is covariant with respect to an irreducible representation of SU(2), and use this representation to analyze the evolution of a quantum directional reference frame when it is exploited as a resource for performing quantum operations. We introduce the moments of a quantum reference frame, which serve as a complete description of its properties as a frame, and investigate how many times a quantum directional reference frame represented by a spin-j system can be used to perform a certain quantum operation with a given probability of success. We provide a considerable generalization of previous results on degradation of reference frame, from which follows a classification of the dynamics of spin-j system under the repeated action of any covariant map with respect to SU(2). Joint work with Lana Sheridan, Martin Laforest and Stephen Bartlett Jean Christian Boileau http://streamer.perimeterinstitute.ca/mp3/ec8f60e3-d42d-41a6-80ec-d39eb9caab3f.mp3 Science http://streamer.perimeterinstitute.ca/mp3/ec8f60e3-d42d-41a6-80ec-d39eb9caab3f.mp3 Wed, 24 Oct 2007 16:00:00 -0400 The one clean qubit model is a model of quantum computation in which all but one qubit starts in the maximally mixed state. One clean qubit computers are believed to be strictly weaker than standard quantum computers, but still capable of solving some classically intractable problems. I'll discuss my recent work in collaboration with Peter Shor which shows that evaluating a certain approximation to the Jones polynomial at a fifth root of unity for the trace closure of a braid is a complete problem for the one clean qubit complexity class. Stephen Jordan http://streamer.perimeterinstitute.ca/mp3/26e116cc-d08f-412e-b5d3-6341b3a17f58.mp3 Science http://streamer.perimeterinstitute.ca/mp3/26e116cc-d08f-412e-b5d3-6341b3a17f58.mp3 Wed, 31 Oct 2007 16:00:00 -0400 Renner's global quantum de Finetti theorem establishes that if the state of a quantum system is invariant under permutations of its systems, then almost all of its subsystems are almost in the same state and independent of each other. Motivated by this result, we show that the most straightforward classical analogue of Renner's theorem is false. Joint work with Matthias Christandl (Cambridge). Ben Toner http://streamer.perimeterinstitute.ca/mp3/8174731b-58de-4bf9-bd33-45eda37b5ccf.mp3 Science http://streamer.perimeterinstitute.ca/mp3/8174731b-58de-4bf9-bd33-45eda37b5ccf.mp3 Wed, 07 Nov 2007 16:00:00 -0500 We will compare quantum phase estimation from the point of view of quantum computation and quantum metrology. In the simplest cases, the former can be simplified to a sequential (unentangled) protocol, while the latter is parallel (entangled). We show that both protocols can be formally related with circuit identities and that they respond in exactly the same way to decoherence. We present sequential protocols for optimal estimation and frame synchronization in DQC1. Finally, we introduce new estimation protocols based on nonlinear Hamiltonians. We show that both optimal input states and product states with separable measurements improve the scaling of linear Hamiltonians. We will comment on the effect of decoherence in nonlinear protocols, and the role of entanglement in nonlinear protocols with product states. Sergio Boixo http://streamer.perimeterinstitute.ca/mp3/0e6192a6-3c83-47fc-90b3-1be1de473862.mp3 Science http://streamer.perimeterinstitute.ca/mp3/0e6192a6-3c83-47fc-90b3-1be1de473862.mp3 Wed, 14 Nov 2007 16:00:00 -0500 A class of operations distinct to entangled states shared between more than two parties is their conversion to entangled states shared between fewer parties. The extent to which these can be achieved in the regime of local operations and classical communication provides an operational characterisation of multiparty states, for example in the "entanglement of assistance" and related quantities. I will give a brief overview of this topic and discuss our results showing qualitatively different behaviour when the parties receiving the final state are not chosen beforehand. Benjamin Fortescue http://streamer.perimeterinstitute.ca/mp3/d8dc2652-5866-4e51-8ec1-5bed4dc10759.mp3 Science http://streamer.perimeterinstitute.ca/mp3/d8dc2652-5866-4e51-8ec1-5bed4dc10759.mp3 Wed, 21 Nov 2007 16:00:00 -0500 We attempt at characterizing the correlations present in the quantum computational model DQC1, introduced by Knill and Laflamme [Phys. Rev. Lett. 81, 5672 (1998)]. The model involves a collection of qubits in the completely mixed state coupled to a single control qubit that has nonzero purity. Although there is little or no entanglement between two parts of this system, it provides an exponential speedup in certain problems. On the contrary, we find that the quantum discord across the most natural split is nonzero for typical instances of the DQC1 ciruit. Nonzero values of discord indicate the presence of nonclassical correlations. We propose quantum discord as figure of merit for characterizing the resources present in this computational model. This might be a complementary measure for counting resources in quantum information science. Animesh Datta http://streamer.perimeterinstitute.ca/mp3/f513ec06-d10f-4b27-96f5-8146316d8a74.mp3 Science http://streamer.perimeterinstitute.ca/mp3/f513ec06-d10f-4b27-96f5-8146316d8a74.mp3 Wed, 28 Nov 2007 16:00:00 -0500 Roughly speaking, the more Alice is entangled with Bob, the harder it is for her to send her state to Charlie. In particular, it will be shown that the squashed entanglement, a well known entanglement measure, gives the fastest rate at which a quantum state can be sent between two parties who share arbitrary side information. Likewise, the entanglement of formation and entanglement cost is shown to be the fastest rate at which a quantum state can be sent when the parties have access to side-information which is maximally correlated. A further restriction on the type of side-information implies that the rate of state transmission is given by the quantum mutual information. This suggests a new paradigm for understanding entanglement and other correlations in terms of quantum Shannon theroy. Different types of side-information correspond to different types of correlations with the squashed entanglement and the mutual information being two extremes. Furthermore, there is a dual paradigm: if one distributes the side-information as aliciously as possible so as to make the sending of the state as difficult as possible, one finds maximum rates which give interpretations to known quantities as well as new ones. Jonathan Oppenheim http://streamer.perimeterinstitute.ca/mp3/29ad893a-c147-4077-9fc8-b8f405186ab9.mp3 Science http://streamer.perimeterinstitute.ca/mp3/29ad893a-c147-4077-9fc8-b8f405186ab9.mp3 Wed, 12 Dec 2007 16:00:00 -0500 We use a Bayesian approach to optimally solve problems in noisy binary search. We deal with two variants: 1. Each comparison can be erroneous with some probability 1 - p. 2. At each stage k comparisons can be performed in parallel and a noisy answer is returned. We present a (classic) algorithm which optimally solves both variants together, up to an additive term of O(log log (n)), and prove matching information theoretic lower bounds. We use the algorithm with the results of Farhi et al. (FGGS99)presenting a quantum search algorithm in an ordered list of expected complexity less than log(n)/3, and some improved quantum lower bounds on noisy search, and search with an error probability. Joint work with Michael Ben-Or. Avinatan Hassidim http://streamer.perimeterinstitute.ca/mp3/4c0f36c7-d558-462c-812e-8b4dd7d64231.mp3 Science http://streamer.perimeterinstitute.ca/mp3/4c0f36c7-d558-462c-812e-8b4dd7d64231.mp3 Wed, 09 Jan 2008 16:00:00 -0500 In this talk, we will investigate the distinguishability of quantum operations from both discrete and continuous point of view. In the discrete case, the main topic is how we can identify quantum measurement apparatuses by considering the patterns of measurement outcomes. In the continuous case, we will focus on the efficiency of parameter estimation of quantum operations. We will discuss several methods that can achieve Heisenberg Limit and prove in some other cases the impossibility of breaking the Standard Quantum Limit. The general treatment of estimation of quantum operations also allows an investigation of the effect of noise on estimation efficiency. Zhengfeng Ji http://streamer.perimeterinstitute.ca/mp3/42548b49-d417-4731-957c-1b3bb731e1fd.mp3 Science http://streamer.perimeterinstitute.ca/mp3/42548b49-d417-4731-957c-1b3bb731e1fd.mp3 Wed, 16 Jan 2008 16:00:00 -0500 The renormalization group (RG) is one of the conceptual pillars of statistical mechanics and quantum field theory, and a key theoretical element in the modern formulation of critical phenomena and phase transitions. RG transformations are also the basis of numerical approaches to the study of low energy properties and emergent phenomena in quantum many-body systems. In this colloquium I will introduce the notion of \"entanglement renormalization\" and use it to define a coarse-graining transformation for quantum systems on a lattice [G.Vidal, Phys. Rev. Lett. 99, 220405 (2007)]. The resulting real-space RG approach is able to numerically address 1D and 2D lattice systems with thousands of quantum spins using only very modest computational resources. From the theoretical point of view, entanglement renormalization sheds new light into the structure of correlations in the ground state of extended quantum systems. I will discuss how it leads to a novel, efficient representation for the ground state of a system at a quantum critical point or with topological order. Guifre Vidal http://streamer.perimeterinstitute.ca/mp3/cb38a649-2c00-4d5d-9b5f-deb5cbd48cc2.mp3 Science http://streamer.perimeterinstitute.ca/mp3/cb38a649-2c00-4d5d-9b5f-deb5cbd48cc2.mp3 Wed, 23 Jan 2008 16:00:00 -0500 We construct a simple translationally invariant, nearest-neighbor Hamiltonian on a chain of 10-dimensional qudits that makes it possible to realize universal quantum computing without any external control during the computational process, requiring only initial product state preparation. Both the quantum circuit and its input are encoded in an initial canonical basis state of the qudit chain. The computational process is then carried out by the autonomous Hamiltonian time evolution. After a time greater than a polynomial in the size of the quantum circuit has passed, the result of the computation can be obtained with high probability by measuring a few qudits in the computational basis. This result also implies that there cannot exist efficient classical simulation methods for generic translationally invariant nearest-neighbor Hamiltonians on qudit chains, unless quantum computers can be efficiently simulated by classical computers (or, put in complexity theoretic terms, unless BPP=BQP). This is joint work with Daniel Nagaj. Pawel Wocjan http://streamer.perimeterinstitute.ca/mp3/7917822b-b46e-4101-9b2a-cd9baf6635b4.mp3 Science http://streamer.perimeterinstitute.ca/mp3/7917822b-b46e-4101-9b2a-cd9baf6635b4.mp3 Wed, 30 Jan 2008 16:00:00 -0500 The \"frequency comb\" defined by the eigenmodes of an optical resonator is a naturally large set of exquisitely well defined quantum systems, such as in the broadband mode-locked lasers which have redefined time/frequency metrology and ultra precise measurements in recent years. High coherence can therefore be expected in the quantum version of the frequency comb, in which nonlinear interactions couple different cavity modes, as can be modeled by different forms of graph states. We show that is possible to thereby generate states of interest to quantum metrology and computing, such as multipartite entangled cluster and Greenberger-Horne-Zeilinger states. Olivier Pfister http://streamer.perimeterinstitute.ca/mp3/ea50dd02-ec63-4d10-9811-b961055d0b73.mp3 Science http://streamer.perimeterinstitute.ca/mp3/ea50dd02-ec63-4d10-9811-b961055d0b73.mp3 Wed, 06 Feb 2008 16:00:00 -0500 I should like to show how particular mathematical properties can limit our metaphysical choices, by discussing old and new theorems within the statistical-model framework of Mielnik, Foulis & Randall, and Holevo, and what these theorems have to say about possible metaphysical models of quantum mechanics. Time permitting, I should also like to show how metaphysical assumptions lead to particular mathematical choices, by discussing how the assumption of space as a relational concept leads to a not widely known frame-invariant formulation of classical point-particle mechanics by Föppl and Zanstra, and related research topics in continuum mechanics and general relativity. PierGianLuca Porta Mana http://streamer.perimeterinstitute.ca/mp3/4964230a-592e-4d62-83df-493707da4cfc.mp3 Science http://streamer.perimeterinstitute.ca/mp3/4964230a-592e-4d62-83df-493707da4cfc.mp3 Wed, 13 Feb 2008 16:00:00 -0500 Decoherence attempts to explain the emergent classical behaviour of a quantum system interacting with its quantum environment. In order to formalize this mechanism we introduce the idea that the information preserved in an open quantum evolution (or channel) can be characterized in terms of observables of the initial system. We use this approach to show that information which is broadcast into many parts of the environment can be encoded in a single observable. This supports a model of decoherence where the pointer observable can be an arbitrary positive operator-valued measure (POVM). This generalization makes it possible to characterize the emergence of a realistic classical phase-space. In addition, this model clarifies the relations among the information preserved in the system, the information flowing from the system to the environment (measurement), and the establishment of correlations between the system and the environment. Cedric Beny http://streamer.perimeterinstitute.ca/mp3/ae72b710-7a2d-4d55-956b-25a1195e8352.mp3 Science http://streamer.perimeterinstitute.ca/mp3/ae72b710-7a2d-4d55-956b-25a1195e8352.mp3 Wed, 27 Feb 2008 16:00:00 -0500 Coin flipping by telephone (Blum '81) is one of the most basic cryptographic tasks of two-party secure computation. In a quantum setting, it is possible to realize (weak) coin flipping with information theoretic security. Quantum coin flipping has been a longstanding open problem, and its solution uses an innovative formalism developed by Alexei Kitaev for mapping quantum games into convex optimization problems. The optimizations are carried out over duals to the cone of operator monotone functions, though the mapped problem can also be described in a very simple language that involves moving points in the plane. Time permitting, I will discuss both Kitaev's formalism, and the solution that leads to quantum weak coin flipping with arbitrarily small bias. Carlos Mochon http://streamer.perimeterinstitute.ca/mp3/6a57b826-abbb-4cf2-b0c3-aa7e871e2afc.mp3 Science http://streamer.perimeterinstitute.ca/mp3/6a57b826-abbb-4cf2-b0c3-aa7e871e2afc.mp3 Wed, 05 Mar 2008 16:00:00 -0500 The talk concerns a generalization of the concept of a minimum uncertainty state to the finite dimensional case. Instead of considering the product of the variances of two complementary observables we consider an uncertainty relation involving the quadratic Renyi entropies summed over a full set of mutually unbiased bases (MUBs). States which achieve the lower bound set by this inequality were introduced by Wootters and Sussman, who proved existence for every prime power dimension, and by Appleby, Dang and Fuchs who showed that in prime dimension the fiducial vector for a for a symmetric informationally complete positive operator valued measure (SIC-POVM) covariant under the Weyl-Heisenberg group is a state of this kind. Subsequently Sussman proved existence for a class of odd prime power dimensions. The purpose of this talk is to complete the existence proof by showing that minimum uncertainty states exist in every prime power dimension, without exception. Along the way we establish a number of properties of the Clifford group, and Galois extension fields, which might be of some independent interest. Marcus Appleby http://streamer.perimeterinstitute.ca/mp3/ac201f51-7225-4e9d-9d0f-27730061b92a.mp3 Science http://streamer.perimeterinstitute.ca/mp3/ac201f51-7225-4e9d-9d0f-27730061b92a.mp3 Wed, 26 Mar 2008 16:00:00 -0400 The Hamiltonian of traditionally adopted detector models features out of diagonal elements between the vacuum and the one particle states of the field to be detected. We argue that reasonably good detectors, when written in terms of fundamental fields, have a more trivial response on the vacuum. In particular, the model configuration ``detector in its ground state + vacuum of the field' generally corresponds to a stable bound state of the underlying theory (e.g. the hydrogen atom in a suitable QED with electrons and protons) and therefore should be also an eigenstate of the model Hamiltonian. As a concrete example, we study a consistent ``fundamental' toy field theory where a stable particle can capture a light quantum and form a quasi-stable state. To such stable particle correspond eigenstates of the full theory, as is shown explicitly by using a dressed particle formalism at first order in perturbation theory. We then write the corresponding Hamiltonian for a model detector (at rest) where the stable particle and the quasi-stable configurations correspond to the two internal levels, ``ground' and ``excited', of the detector. The accelerated version of this Hamiltonian is inevitably model dependent emph{i.e.} it will generally depend on how the stable particle/detector is forced along the accelerated trajectory. However, in its most basic version, the accelerated detector doesn't see Unruh radiation. Federico Piazza http://streamer.perimeterinstitute.ca/mp3/acb0b7c0-890c-4e94-8986-68614a32fcf8.mp3 Science http://streamer.perimeterinstitute.ca/mp3/acb0b7c0-890c-4e94-8986-68614a32fcf8.mp3 Wed, 30 Apr 2008 16:00:00 -0400 Wigner-Dirac relativistic quantum theory is applied to decay laws of an unstable particle in different reference frames. It is shown that decay slows down from the point of view of the moving observer, as expected. However, small deviations from Einstein's time dilation formula are also found. The origin of these deviations is discussed, as well as possibilities for their experimental detection. Eugene Stefanovich http://streamer.perimeterinstitute.ca/mp3/de8fc09c-5412-488a-9aa3-4527aa6718ac.mp3 Science http://streamer.perimeterinstitute.ca/mp3/de8fc09c-5412-488a-9aa3-4527aa6718ac.mp3 Wed, 07 May 2008 11:00:00 -0400 What does a fractional quantum Hall liquid and Kitaev's proposals for topological quantum computation have in common? It turns out that they are physical systems that exhibit degenerate ground states with properties seemingly different than ordinary (Landau-type) vacua, such as the ground states of a Heisenberg magnet. For example, those (topologically quantum ordered)states cannot be characterized by (local) order parameters such as magnetization. How does one characterize this new order? I will present a unifying framework which will allow us to engineer physical systems displaying topological quantum order. What are the physical properties of these new orders? How robust are they to temperature effects? What are they useful for? Topologically quantum ordered states of matter seem to be ideal physical systems to store and manipulate quantum information since they are believed to be robust against decoherence with an environment, and thus appropriate for building a quantum computer and quantum memories. I will discuss the role of temperature in the protection of quantum information. Have we finally found a technological application for quantum Hall liquids? Gerardo Ortiz http://streamer.perimeterinstitute.ca/mp3/cbc8c7a3-a522-438b-b042-1c0dd8c8196d.mp3 Science http://streamer.perimeterinstitute.ca/mp3/cbc8c7a3-a522-438b-b042-1c0dd8c8196d.mp3 Wed, 07 May 2008 16:00:00 -0400 In an effort to better understand the class of operations on a bipartite system which preserve positivity of partial transpose (PPT operations), we have investigated the (non-asymptotic) transformation of pure states to pure states by operations in this class. Under local operations and classical communication (LOCC) Nielsen's majorization criterion provides a necessary and sufficient condition for such a transformation. This can be used to show that under LOCC a phenomenon called catalysis can occur, where an otherwise impossible transformation can be made possible by the provision of an entangled catalyst state, which must be recovered unchanged after the transformation (hence the name). I will present some recent work where we have found a necessary condition for obtaining a given pure state from a maximally entangled state via PPT operations. This condition is conjectured to be sufficient also, and we can prove this for the case where the goal state has Schmidt rank three. We have also shown that catalysis occurs under PPT operations, and have derived a necessary and sufficient condition for PPT pure state transformations where both the initial state and the catalyst are maximally entangled. Will Matthews http://streamer.perimeterinstitute.ca/mp3/5e4f3ce5-f50a-4f49-9970-f37be9625430.mp3 Science http://streamer.perimeterinstitute.ca/mp3/5e4f3ce5-f50a-4f49-9970-f37be9625430.mp3 Wed, 14 May 2008 16:00:00 -0400 We discuss two methods to encode one qubit into six physical qubits. Each of our two examples corrects an arbitrary single-qubit error. Our first example is a degenerate six-qubit quantum error-correcting code. We explicitly provide the stabilizer generators, encoding circuits, codewords, logical Pauli operators, and logical CNOT operator for this code. We also show how to convert this code into a non-trivial subsystem code that saturates the subsystem Singleton bound. We then prove that a six-qubit code without entanglement assistance cannot simultaneously possess a Calderbank-Shor-Steane (CSS) stabilizer and correct an arbitrary single-qubit error. A corollary of this result is that the Steane seven-qubit code is the smallest single-error correcting CSS code. Our second example is the construction of a non-degenerate six-qubit CSS entanglement-assisted code. This code uses one bit of entanglement (an ebit) shared between the sender and the receiver and corrects an arbitrary single-qubit error. The code we obtain is globally equivalent to the Steane seven-qubit code and thus corrects an arbitrary error on the receiver's half of the ebit as well. We prove that this code is the smallest code with a CSS structure that uses only one ebit and corrects an arbitrary single-qubit error on the sender's side. We discuss the advantages and disadvantages for each of the two codes. Bilal Shaw http://streamer.perimeterinstitute.ca/mp3/b495de84-4a66-41d9-867e-b320a9cbecb1.mp3 Science http://streamer.perimeterinstitute.ca/mp3/b495de84-4a66-41d9-867e-b320a9cbecb1.mp3 Wed, 09 Jul 2008 16:00:00 -0400 One of the quintessential features of quantum information is its exclusivity, the inability of strong quantum correlations to be shared by many physical systems. Likewise, complementarity has a similar status in quantum mechanics as the sine qua non of quantum phenomena. We show that this is no coincidence, and that the central role of exclusivity in quantum information theory stems from the phenomenon of complementarity. We adopt an information-theoretic approach to complementarity, which leads to a new and simple definition of private states and new proofs of the achievable asymptotic rates of both secret key and entanglement distillation. From the latter follows a new proof of the direct part of the quantum noisy channel coding theorem. Joseph Renes http://streamer.perimeterinstitute.ca/mp3/215528bd-b779-4c87-b4a5-ed76049e7e8c.mp3 Science http://streamer.perimeterinstitute.ca/mp3/215528bd-b779-4c87-b4a5-ed76049e7e8c.mp3 Wed, 13 Aug 2008 16:00:00 -0400 I will report on efforts to implement a new method for simulating concatenated quantum error correction, where many levels of concatenation are simulated together explicitly. That is, the approach involves a Monte Carlo simulation of a noisy circuit involving many thousands of qubits, rather than tens of qubits previously. The new approach allows the threshold and resource usage of concatenated quantum error correction to be determined more accurately than before. Also, the approach makes it possible to better study the effects of circuit optimizations and message-passing algorithms [Poulin, PRA, 2006] on the performance of fault-tolerant concatenated quantum error correction. Such studies are necessary in order make a proper comparison with competing families of error-correction protocols, such as those involving surface codes. In the talk, a range of new numerical results will be presented. Henry Haselgrove http://streamer.perimeterinstitute.ca/mp3/a9f5d6ab-d1f8-4322-a16e-ef16212260ae.mp3 Science http://streamer.perimeterinstitute.ca/mp3/a9f5d6ab-d1f8-4322-a16e-ef16212260ae.mp3 Wed, 17 Sep 2008 16:00:00 -0400 A quantum channel models a physical process in which noise is added to a quantum system via interaction with its environment. Protecting quantum systems from such noise can be viewed as an extension of the classical communication problem introduced by Shannon sixty years ago. A fundamental quantity of interest is the quantum capacity of a given channel, which measures the amount of quantum information which can be protected, in the limit of many transmissions over the channel. In this talk, I will show that certain pairs of channels, each with a capacity of zero, can have a strictly positive capacity when used together, implying that the quantum capacity does not completely characterize a channel's ability to transmit quantum information. As a corollary, I will show that a commonly used lower bound on the quantum capacity - the coherent information, or hashing bound - is an overly pessimistic benchmark against which to measure the performance of quantum error correction because the gap between this bound and the capacity can be arbitrarily large. Jon Yard http://streamer.perimeterinstitute.ca/mp3/f4834b0b-218b-4d27-927e-82a4a87297f9.mp3 Science http://streamer.perimeterinstitute.ca/mp3/f4834b0b-218b-4d27-927e-82a4a87297f9.mp3 Wed, 24 Sep 2008 16:00:00 -0400 In this talk I will give an introduction to the simulation of quantum many-body systems using the so-called tensor networks. After a brief historical review, I will introduce the basics on tensor network representations of quantum states, and will explain some recent developments. In particular, in the last part of my talk I will focus on recent results obtained in the simulation of 2-dimensional quantum lattice systems of infinite size. Roman Orus http://streamer.perimeterinstitute.ca/mp3/fafdfd3b-a523-4e7b-bd53-b10ce39d8b23.mp3 Science http://streamer.perimeterinstitute.ca/mp3/fafdfd3b-a523-4e7b-bd53-b10ce39d8b23.mp3 Wed, 08 Oct 2008 16:00:00 -0400 I would like to provide a short, possibly elementary, introduction to the problem of computing string amplitudes at higher genus for superstrings. Essentially, I will recall which is the mathematical problem in defining the path integral measure (which has a well defined algebraic geometry realization for bosonic strings) and the solution proposed by d~@~YHocker and Phong for the genus 2 case. Their main results are the chiral splitted form of the measure, and its explicit expression in genus two. They proposed the splitting form to work at any genus and assumed some restriction for the explicit form which however did not permitted them to find a solution for genera higher then 2. I will tell something about the technology which permitted us to find explicit solutions for genus 3 and four. Indeed, we showed that the restrictions imposed by d~@~YHocker and Phong have no solution whereas the most general form compatible with modular invariance and clustering provide a unique solution, at least for genus 3 and 4. I will try to be as less technical as possible. Sergio Cacciatori http://streamer.perimeterinstitute.ca/mp3/ad345c70-6617-42ef-9851-fdcc364fa197.mp3 Science http://streamer.perimeterinstitute.ca/mp3/ad345c70-6617-42ef-9851-fdcc364fa197.mp3 Thu, 09 Oct 2008 14:00:00 -0400 The rise of quantum information science has been paralleled by the development of a vigorous research program aimed at obtaining an informational characterization or reconstruction of the quantum formalism, in a broad framework for stochastic theories that encompasses quantum and classical theory, but also a wide variety of other theories that can serve as foils to them. Such a reconstruction, at its most ambitious, is envisioned as playing a role in quantum physics similar to Einstein's reconstruction of the dynamics and kinetics of macroscopic bodies, and later of their gravitational interactions, on the basis of simple principles with clear operational meanings and experimental consequences. But short of such an ambitious goal, it could still lead to a principled understanding of the features of quantum mechanics that account for its greater-than-classical information-processing power, an understanding which could help guide the search for new quantum algorithms and protocols. I will summarize a convex operational framework for possible physical theories, and present results from a project to characterize quantum mechanics in terms of principles tightly linked to the possibility or impossibility of various information processing protocols. Previous results identified properties, like the existence of information-disturbance tradeoffs and restrictions on cloning and broadcasting, common to all nonclassical theories. In this talk I will focus on recent results involving protocols that are less generic. These are: the existence of exponentially secure bit commitment in non-classical theories without entanglement, the consequences for theories of the existence of a conclusive teleportation scheme, and sufficient conditions for the existence of a deterministic teleportation scheme. I'll also discuss sufficient conditions for 'remote steering' of ensembles using entanglement, rendering insecure bit commitment protocols of the form shown to be secure in the unentangled case. Connections to the category-theoretic approach of Coecke and Abramsky, Selinger, Baez, and collaborators may be touched on if time permits. Joint work with various groups of collaborators including Jonathan Barrett, Matthew Leifer, Alexander Wilce, Oscar Dahlsten, and Ben Toner. Howard Barnum http://streamer.perimeterinstitute.ca/mp3/9b5ba30b-6b7a-4443-88e7-6c05f644c002.mp3 Science http://streamer.perimeterinstitute.ca/mp3/9b5ba30b-6b7a-4443-88e7-6c05f644c002.mp3 Wed, 15 Oct 2008 16:00:00 -0400 We study the possibility of a self-correcting quantum memory based on stabilizer codes with geometrically-local stabilizer generators. We prove that the distance of such stabilizer codes in D dimensions is bounded by O(L^{D-1}) where L is the linear size of the D-dimensional lattice. In addition, we prove that in D=1 and D=2, the energy barrier separating different logical states is upper-bounded by a constant independent of L. This shows that in such systems there is no natural energy dissipation mechanism which prevents errors from accumulating. Our results are in contrast with the existence of a classical 2D self-correcting memory, the 2D Ising ferromagnet. Barbara Terhal http://streamer.perimeterinstitute.ca/mp3/e9ee62f7-f7f0-45f5-abb1-0da8e460d1ee.mp3 Science http://streamer.perimeterinstitute.ca/mp3/e9ee62f7-f7f0-45f5-abb1-0da8e460d1ee.mp3 Wed, 22 Oct 2008 16:00:00 -0400 We analyze how quantum complexity poses bounds to the simulation of quantum systems. While methods as Density Functional Theory (DFT) and the Density Matrix Renormalization Group (DMRG) work very well in practice, essentially nothing on the formal requirements is known. In this talk, we consider these methods from a quantum complexity perspective: First, we discuss DFT which encapsulates the difficulty of solving the Schroedinger equation in a universal functional and show that this functional cannot be efficiently computed unless several complexity classes collapse. Second, we consider DMRG, a method to deal with quantum spin chains, and show that even under reasonable assumptions -- a polynomial gap and matrix product ground states -- finding the ground state is still a computationally hard problem. Beyond pinpointing the limitations of the methods, this helps us to understand under which assumptions we might be able to prove their convergence. Norbert Schuch http://streamer.perimeterinstitute.ca/mp3/e2311fef-bb80-47de-b7d7-5201494f2cf6.mp3 Science http://streamer.perimeterinstitute.ca/mp3/e2311fef-bb80-47de-b7d7-5201494f2cf6.mp3 Wed, 05 Nov 2008 16:00:00 -0500 By storing quantum information in the degenerate ground state of a Hamiltonian, it is hoped that it can be made quite robust against noise processes. We will examine this situation, with particular emphasis on the Toric code in 2D, and show how adversarial effects, either perturbations to the Hamiltonian or interactions with an environment, destroy the stored information extremely quickly. Alastair Kay http://streamer.perimeterinstitute.ca/mp3/c590da62-6b01-4511-960a-441362afec6a.mp3 Science http://streamer.perimeterinstitute.ca/mp3/c590da62-6b01-4511-960a-441362afec6a.mp3 Wed, 12 Nov 2008 16:00:00 -0500 Quantum computation by single-qubit measurements was proposed by Raussendorf and Briegel [PRL 86, 5188] as a potential scheme for implementing quantum computers. It also offers an unusual means of describing unitary transformations. To better understand which measurement-based procedures perform unitary operations, we may consider the following problem: under what circumstances can a measurement-based procedure for a unitary U be found, provided a similar procedure for U which relies on post-selection? In this talk, I describe the so-called 'Measurement Pattern Interpolation' problem, the intuition behind the solved special cases, and possible applications of a general solution to this problem. Niel de Beaudrap http://streamer.perimeterinstitute.ca/mp3/16c89932-4947-445e-beaf-af1066b58313.mp3 Science http://streamer.perimeterinstitute.ca/mp3/16c89932-4947-445e-beaf-af1066b58313.mp3 Wed, 19 Nov 2008 16:00:00 -0500 With the aim of proposing feasible, quantum optical realizations of quantum information protocols and minimizing the resource costs in such implementations, we will discuss various, so-called hybrid approaches. These include, for instance, schemes based upon both discrete and continuous quantum variables. Peter van Loock http://streamer.perimeterinstitute.ca/mp3/7fac3bdf-cc72-4730-b44c-2ef6c62cd77a.mp3 Science http://streamer.perimeterinstitute.ca/mp3/7fac3bdf-cc72-4730-b44c-2ef6c62cd77a.mp3 Wed, 26 Nov 2008 16:00:00 -0500 In recent years, the analysis of boolean functions has arisen as an important theme in theoretical computer science. In this talk I will discuss an extension of the concept of a boolean function to quantum computation. It turns out that many important classical results in the theory of boolean functions have natural quantum analogues. These include property testing of boolean functions; the Goldreich-Levin algorithm for approximately learning boolean functions; and a theorem of Friedgut, Kalai and Naor on the Fourier spectra of boolean functions. The quantum generalisation of this theorem uses a quantum extension of the hypercontractive inequality of Bonami, Gross and Beckner. This talk is based on joint work with Tobias Osborne. Ashley Montanaro http://streamer.perimeterinstitute.ca/mp3/7a8743cf-e56f-42f3-ad70-d01b26958889.mp3 Science http://streamer.perimeterinstitute.ca/mp3/7a8743cf-e56f-42f3-ad70-d01b26958889.mp3 Wed, 03 Dec 2008 16:00:00 -0500 We introduce a two-body quantum Hamiltonian model of spin-1/2 on a 2D spatial lattice with exact topological degeneracy in all coupling regimes. There exists a gapped phase in which the low-energy sector reproduces an effective color code model. High energy excitations fall into three families of anyonic fermions that turn out to be strongly interacting. The model exhibits a Z_2xZ_2 gauge group symmetry and string-net integrals of motion, which are related to the existence of topological charges that are invisible to moving high-energy fermions. Hector Bombin http://streamer.perimeterinstitute.ca/mp3/ba57b58b-6604-4494-8078-9f35f051efce.mp3 Science http://streamer.perimeterinstitute.ca/mp3/ba57b58b-6604-4494-8078-9f35f051efce.mp3 Wed, 21 Jan 2009 16:00:00 -0500 Recent results have shown that quantum computers can approximate the value of a tensor network efficiently. These results have initiated a search for tensor networks which contract to computationally interesting quantities. Topological Lattice Field Theories (TLFTs) are one source of such networks; when defined appropriately, networks arising from TLFTs contract to give topological invariants. In this elementary talk, we will define and classify TLFTs which lead to invariants of surfaces, and sketch out the corresponding quantum algorithm. Our exposition will be targetted at a general mathematically-inclined audience; no previous knowledge of field theories is required. Gorjan Alagic http://streamer.perimeterinstitute.ca/mp3/0a4283fb-52f8-4c94-a695-4ecfaad8cbad.mp3 Science http://streamer.perimeterinstitute.ca/mp3/0a4283fb-52f8-4c94-a695-4ecfaad8cbad.mp3 Wed, 04 Feb 2009 16:00:00 -0500 Suppose we are given two probability distributions on some N-element set. How many samples do we need to test whether the two distributions are close or far from each other in the L_1 norm? This problem known as Statistical Difference has been extensively studied during the last years in the field of property testing. I will describe quantum algorithms for Statistical Difference problem that provide a polynomial speed up in terms of the query complexity compared to the known classical lower bounds. Specifically, I will assume that each distribution can be generated by querying an oracle function on a random uniformly distributed input string. It will be shown that testing whether distributions are orthogonal requires approximately N^{1/2} queries classically and approximately N^{1/3} queries quantumly. Testing whether distributions are close requires approximately N^{2/3} queries classically and O(N^{1/2}) queries quantumly. This is a joint work with Aram Harrow (University of Bristol) and Avinatan Hassidim (The Hebrew University). Sergey Bravyi http://streamer.perimeterinstitute.ca/mp3/4d2778b3-d092-40bd-8d38-5040a846d3aa.mp3 Science http://streamer.perimeterinstitute.ca/mp3/4d2778b3-d092-40bd-8d38-5040a846d3aa.mp3 Wed, 18 Feb 2009 16:00:00 -0500 In topological quantum computation the geometric details of a particle trajectory become irrelevant; only the topology matters. This is one reason for the inherent fault tolerance of topological quantum computation. I will speak about a model in which this idea is taken one step further. Even the topology is irrelevant. The computation is determined solely by the permutation of the particles. Unlike topological quantum computation, which requires anyons confined to two dimensions, permutational quantum computations can in principle be performed by permuting a set of ordinary spin-1/2 particles with definite total angular momentum in three dimensions. The resulting model of computation appears to be intermediate in power between classical computation (P) and standard quantum computation (BQP). The model may be equivalently defined in terms of spin networks, which are an important concept in loop quantum gravity. Stephen Jordan http://streamer.perimeterinstitute.ca/mp3/ef1896ab-5887-49c0-a88d-a64bdd593557.mp3 Science http://streamer.perimeterinstitute.ca/mp3/ef1896ab-5887-49c0-a88d-a64bdd593557.mp3 Wed, 04 Mar 2009 16:00:00 -0500 We study the entanglement dynamics and relaxation properties of a system of two interacting qubits in the two cases (I) two independent bosonic baths and (II) one common bath, at temperature $T$. The entanglement dynamics is studied in terms of the concurrence C(t) between the two spins and of the von Neumann entropy S(t) with respect to the bath, as a function of time. We prove that the system does thermalize. In the case (II) of a single bath, the existence of a decoherence-free (DFS) subspace makes entanglement dynamics very rich. We show that when the system is initially in a state with a component in the DFS the relaxation time is surprisingly long, showing the existence of semi-decoherence free subspaces. The equilibrium state in this case is not the Gibbs state. The entanglement dynamics for the single bath case is also studied as a function of temperature, coupling strength with the environment and strength of tunneling coupling. The case of the mixed state is finally shown and discussed. Alioscia Hamma http://streamer.perimeterinstitute.ca/mp3/242dbef1-fc5a-4fe9-8de4-4a0a91f02bb2.mp3 Science http://streamer.perimeterinstitute.ca/mp3/242dbef1-fc5a-4fe9-8de4-4a0a91f02bb2.mp3 Mon, 23 Mar 2009 16:00:00 -0400 Quantum random walks have received much interest due to their non- intuitive dynamics, which may hold a key to radically new quantum algorithms. What remains a major challenge is a physical realization that is experimentally viable, readily scalable, and not limited to specific connectivity criteria. In this seminar, I will present an implementation scheme for quantum walking on arbitrarily complex graphs. This scheme is particularly elegant since the walker is not required to physically step between the nodes; only flipping coins is sufficient. In addition, by taking advantage of the inherent structure of the CS decomposition of unitary matrices, we are able to implement all coin operations necessary for each step of the walk simultaneously. This scheme can be physically realized using a variety of quantum systems, such as cold atoms trapped inside an optical lattice or electrons inside coupled quantum dots. Jingbo Wang http://streamer.perimeterinstitute.ca/mp3/9a085784-7b4f-4d33-97e3-a7ea8e703749.mp3 Science http://streamer.perimeterinstitute.ca/mp3/9a085784-7b4f-4d33-97e3-a7ea8e703749.mp3 Wed, 06 May 2009 16:00:00 -0400 A fully general strong converse for channel coding states that when the rate of sending classical information exceeds the capacity of a quantum channel, the probability of correctly decoding goes to zero exponentially in the number of channel uses, even when we allow code states which are entangled across several uses of the channel. Such a statement was previously only known for classical channels and the quantum identity channel. By relating the problem to the additivity of minimum output entropies, we show that a strong converse holds for a large class of channels, including all unital qubit channels, the d-dimensional depolarizing channel and the Werner-Holevo channel. This further justifies the interpretation of the classical capacity as a sharp threshold for information-transmission. Joint work with Robert Koenig. Stephanie Wehner http://streamer.perimeterinstitute.ca/mp3/3ad463af-28a7-4b4f-bdaa-a098ebc54284.mp3 Science http://streamer.perimeterinstitute.ca/mp3/3ad463af-28a7-4b4f-bdaa-a098ebc54284.mp3 Wed, 20 May 2009 16:00:00 -0400 This talk will present an overview of work done in the past decade on quantum state and process tomography, describing the basic notions at an introductory level, and arguing for a pragmatic approach for data reconstruction. The latest results include recent numerical comparison of different reconstruction techniques, aimed at answering the question: "is 'the best' the enemy of 'good enough'?" Daniel James http://streamer.perimeterinstitute.ca/mp3/b2a8456c-7c44-41ab-9800-db046ccc579e.mp3 Science http://streamer.perimeterinstitute.ca/mp3/b2a8456c-7c44-41ab-9800-db046ccc579e.mp3 Wed, 03 Jun 2009 16:00:00 -0400 We review situations under which standard quantum adiabatic conditions fail. We reformulate the problem of adiabatic evolution as the problem of Hamiltonian eigenpath traversal, and give cost bounds in terms of the length of the eigenpath and the minimum energy gap of the Hamiltonians. We introduce a randomized evolution method that can be used to traverse the eigenpath and show that a standard adiabatic condition is recovered. We then describe more efficient methods for the same task and show that their implementation complexity is close to optimal. Sergio Boixo http://streamer.perimeterinstitute.ca/mp3/f52a1e9e-4431-4ec9-90ba-92191183074d.mp3 Science http://streamer.perimeterinstitute.ca/mp3/f52a1e9e-4431-4ec9-90ba-92191183074d.mp3 Wed, 12 Aug 2009 16:00:00 -0400 At NIST we are engaged in an experiment whose goal is to create superpositions of optical coherent states (such superpositions are sometimes called "Schroedinger cat" states). We use homodyne detection to measure the light, and we apply maximum likelihood quantum state tomography to the homodyne data to estimate the state that we have created. To assist in this analysis we have made a few improvements to quantum state tomography: we have devised a new iterative method (that has faster convergence than R*rho*R iterations) to find the maximum likelihood state, we have formulated a stopping criterion that can upper-bound the actual maximum likelihood, and we have implemented a bias-corrected resampling strategy to estimate confidence intervals. Scott Glancy http://streamer.perimeterinstitute.ca/mp3/f3a43ae9-f4d3-43bd-b6bd-970b4bc0f878.mp3 Science http://streamer.perimeterinstitute.ca/mp3/f3a43ae9-f4d3-43bd-b6bd-970b4bc0f878.mp3 Wed, 09 Sep 2009 16:00:00 -0400 TBA Dave Bacon http://streamer.perimeterinstitute.ca/mp3/01ddbe0c-e659-4d66-8fcb-27ae609563dc.mp3 Science http://streamer.perimeterinstitute.ca/mp3/01ddbe0c-e659-4d66-8fcb-27ae609563dc.mp3 Mon, 14 Sep 2009 15:00:00 -0400 Adiabatic quantum optimization has attracted a lot of attention because small scale simulations gave hope that it would allow to solve NP-complete problems efficiently. Later, negative results proved the existence of specifically designed hard instances where adiabatic optimization requires exponential time. In spite of this, there was still hope that this would not happen for random instances of NP-complete problems. This is an important issue since random instances are a good model for hard instances that can not be solved by current classical solvers, for which an efficient quantum algorithm would therefore be desirable. Here, we will show that because of a phenomenon similar to Anderson localization, an exponentially small eigenvalue gap appears in the spectrum of the adiabatic Hamiltonian for large random instances, very close to the end of the algorithm. This implies that unfortunately, adiabatic quantum optimization also fails for these instances by getting stuck in a local minimum, unless the computation is exponentially long. Joint work with Boris Altshuler and Hari Krovi Jeremie Roland http://streamer.perimeterinstitute.ca/mp3/4924149a-57cf-431a-ad19-c2207877f1cf.mp3 Science http://streamer.perimeterinstitute.ca/mp3/4924149a-57cf-431a-ad19-c2207877f1cf.mp3 Wed, 07 Oct 2009 16:00:00 -0400 A recent breakthrough in quantum computing has been the realization that quantum computation can proceed solely through single-qubit measurements on an appropriate quantum state. One exciting prospect is that the ground or low-temperature thermal state of an interacting quantum many-body system can serve as such a resource state for quantum computation. The system would simply need to be cooled sufficiently and then subjected to local measurements. It would be unfortunate, however, if the usefulness of a ground or low-temperature thermal state for quantum computation was critically dependent on the details of the system's Hamiltonian; if so, engineering such systems would be difficult or even impossible. A much more powerful result would be the existence of a robust ordered phase which is characterized by the ability to perform measurement-based quantum computation. I’ll discuss some recent results on the existence of such a computational phase of matter. I’ll first outline some positive results on a phase of a toy model that contains the cluster state. Then, in a realistic model of coupled spin-1 particles, I’ll demonstrate the existence of a computational phase. This result is obtained by using a local measurement sequence to “renormalize” the state to a computationally-universal fixed point. Together, these results reveal that the characterization of computational phases of matter has a rich, complex structure – one which is still poorly understood. Joint work with Gavin Brennen, Akimasa Miyake, and Joseph Renes. Stephen Bartlett http://streamer.perimeterinstitute.ca/mp3/74c2ec8a-5d00-4899-a196-07149b67cb3d.mp3 Science http://streamer.perimeterinstitute.ca/mp3/74c2ec8a-5d00-4899-a196-07149b67cb3d.mp3 Wed, 04 Nov 2009 16:00:00 -0500 Dualities appear in nearly all disciplines of physics and play a central role in statistical mechanics and field theory. I will discuss in a pedagogical way our recent findings motivated by a quest for a simple unifying framework for the detection and treatment of dualities. I will explain how classical and quantum dualities, as well as duality relations that appear only in a sector of certain theories (i.e. emergent dualities), can be unveiled, and systematically established. Our method relies on the use of morphisms of the "bond algebra" of a quantum Hamiltonian. Dualities are characterized as unitary mappings implementing such morphisms, whose even powers become symmetries of the quantum problem. Dual variables (non-local mappings between the elementary degrees of freedom of the theory) which were guessed in the past can be derived in our formalism. New self-dualities for four-dimensional Abelian gauge field theories will be discussed. Gerardo Ortiz http://streamer.perimeterinstitute.ca/mp3/2075d0c5-6487-4100-905e-c2fc5165874d.mp3 Science http://streamer.perimeterinstitute.ca/mp3/2075d0c5-6487-4100-905e-c2fc5165874d.mp3 Wed, 18 Nov 2009 16:00:00 -0500 Are Quantum Mechanics and Special Relativity unrelated theories? Is Quantum Field Theory an additional theoretical layer over them? Where the quantization rules and the Plank constant come from? All these questions can find answer in the computational paradigm: "the universe is a huge quantum computer". In my talk I'll take the computational-universe paradigm as genuine theoretical framework, and analyze some relevant implications. A new kind of quantum field theory emerges: "Quantum-Computational Field Theory" (QCFT). I will show how in QCFT Special Relativity unfolds from the fabric of the computational network, which also naturally embeds gauge-invariance, and even the quantization rule and the Planck constant, which thus resort to being properties of the underlying causal tapestry of space-time. In this way Quantum Mechanics remains the only theory needed to describe the computational-universe. I will analyze few simple toy-models in order to explore the mathematical structure of QCFT. The new QCFT has many advantages versus the customary field theoretical framework, solving a number of logical and mathematical problems that plague quantum field theory. One further advantage of QCFT is the possibility of changing the computational engine without changing the field-theoretical framework. One can thus consider different kind of engines, e.g. classical, quantum, super-quantum, and even input-output networks with no pre-established causal relations, which are very interesting for addressing the problem of Quantum Gravity. QCFT opens a large research line: I argue that this program should be addressed soon in the particle physics domain, before entering Quantum Gravity, notwithstanding the experimental success of the usual quantum field theory. It will also be the first test of the Lucien Hardy's program on Quantum Gravity. Reference: arXiv:1001.1088 (http://arxiv.org/abs/1001.1088) Giacomo D'Ariano http://streamer.perimeterinstitute.ca/mp3/0ec53e98-01ff-4d76-8fd9-f02c4909aaec.mp3 Science http://streamer.perimeterinstitute.ca/mp3/0ec53e98-01ff-4d76-8fd9-f02c4909aaec.mp3 Wed, 03 Feb 2010 16:00:00 -0500 In recent years the characterization of many-body ground states via the entanglement of their wave-function has attracted a lot of attention. One useful measure of entanglement is provided by the entanglement entropy S. The interest in this quantity has been sparked, in part, by the result that at one dimensional quantum critical points (QCPs) S scales logarithmically with the subsystem size with a universal coefficient related to the central charge of the conformal field theory describing the QCP. On the other hand, in spatial dimension d > 1 the leading contribution to the entanglement entropy scales as the area of the boundary of the subsystem. The coefficient of this "area law" is non-universal. However, in the neighbourhood of a QCP, S is believed to possess subleading universal corrections. In this talk, I will present the first field-theoretic study of entanglement entropy in dimension d > 1 at a stable interacting QCP - the quantum O(N) model. Our results confirm the presence of universal corrections to the entanglement entropy and exhibit a number of surprises such as different epsilon -> 0 limits of the Wilson-Fisher and Gaussian fixed points, violation of large N counting and subtle dependence on replica index. Max Metlitski http://streamer.perimeterinstitute.ca/mp3/a402386f-2244-467b-9272-f3f360e570f2.mp3 Science http://streamer.perimeterinstitute.ca/mp3/a402386f-2244-467b-9272-f3f360e570f2.mp3 Wed, 03 Mar 2010 16:00:00 -0500 Topological phases in spin systems are exciting frontiers of research with intimate connections to quantum coding theory. However, there is a disconnection between quantum codes and the idea of topology, in the absence of geometry and physical realizability. Here, we introduce a toy model, in which quantum codes are constrained to not only have a local geometric description, but also have translation and scale symmetries. These additional physical constraints enable us to assign topologically invariant properties to geometric shapes of logical operators of the code. Topological phases of the model are analyzed by geometrically classifying logical operators. The classification scheme also has topologically universal properties which are invariant under local unitary transformations and local perturbations, and may explain how global symmetries of a system Hamiltonian give rise to topological phases in correlated spin systems. Beni Yoshida http://streamer.perimeterinstitute.ca/mp3/aac10670-4d39-4f26-9a0d-63e9444282ca.mp3 Science http://streamer.perimeterinstitute.ca/mp3/aac10670-4d39-4f26-9a0d-63e9444282ca.mp3 Wed, 17 Mar 2010 16:00:00 -0400 Shared entanglement between sender and receiver can enable more errors to be corrected than with a standard quantum error-correcting code. This extra error correction can be used either to boost the rate of the code--commonly seen in quantum codes constructed from classical linear codes--or to increase the error-correcting power of the code (as represented by, for example, the code distance). We will see how adding extra entanglement to a given quantum code can increase its distance, and discuss the optimization problem in maximizing the effectiveness of a given amount of added entanglement. We will also briefly examine some applications of entanglement-assistance to particular types of codes, such as LDPC codes and convolutional codes. Todd Brun http://streamer.perimeterinstitute.ca/mp3/65439e50-589f-4188-aba8-ec9a630f33c7.mp3 Science http://streamer.perimeterinstitute.ca/mp3/65439e50-589f-4188-aba8-ec9a630f33c7.mp3 Wed, 14 Apr 2010 16:00:00 -0400 The arrow of time dilemma: the laws of physics are invariant for time inversion, whereas the familiar phenomena we see everyday are not (i.e. entropy increases). I show that, within a quantum mechanical framework, all phenomena which leave a trail of information behind (and hence can be studied by physics) are those where entropy necessarily increases or remains constant. All phenomena where the entropy decreases must not leave any information of their having happened. This situation is completely indistinguishable from their not having happened at all. In the light of this observation, the second law of thermodynamics is reduced to a mere tautology: physics cannot study those processes where entropy has decreased, even if they were commonplace. I will discuss the possible limitations that stem from recent typicality results in employing this as a complete self-consistent solution to the arrow of time dilemma. Lorenzo Maccone http://streamer.perimeterinstitute.ca/mp3/fc2e6d28-338f-4b66-9d52-552b32be7477.mp3 Science http://streamer.perimeterinstitute.ca/mp3/fc2e6d28-338f-4b66-9d52-552b32be7477.mp3 Wed, 28 Apr 2010 16:00:00 -0400 Fibonacci anyons are the simplest system of anyons capable of implementing universal topological quantum computation, an area which is of intense theoretical and experimental interest. Recent studies have shown that for nearest-neighbour interactions, the properties of the ground state of a 1-D chain of Fibonacci anyons may be modeled using a spin chain, and are related to specific conformal field theories. I will talk about the role played by boundary conditions in this mapping, and demonstrate that for these simple anyonic systems the correct spin chain models in fact correspond to conformal field theories with a defect. The presence of this defect drastically changes the excitations observable in the system. Robert Pfeifer http://streamer.perimeterinstitute.ca/mp3/4beb13c5-a26b-4eb3-afd4-bb62660871c2.mp3 Science http://streamer.perimeterinstitute.ca/mp3/4beb13c5-a26b-4eb3-afd4-bb62660871c2.mp3 Wed, 12 May 2010 16:00:00 -0400 In this talk I review some joint work (arXiv:1008.2147) with Bill Munro and Tim Spiller on the task we call "quantum tagging", that is, authenticating the classical location of a classical tagging device by sending and receiving quantum signals from suitably located distant sites, in an environment controlled by an adversary whose quantum information processing and transmitting power is unbounded. Simple security models for this task will be presented. It will be shown that (among other protocols) recent protocols claimed to be unconditionally secure by Malaney and by Chandran et al. can in fact be broken by an adversary with pre-distributed entanglement using teleportation-based attacks. I also describe some protocols which cannot be broken by these specific attacks, but do not prove they are unconditionally secure. From a more foundational perspective, this work can be thought of (i) as an attempt to understand how and when we can know that something is somewhere, and (ii) an introduction to an interesting wider class of (im)possibility questions in relativistic quantum theory. If time permits, I will also touch on these topics. Adrian Kent http://streamer.perimeterinstitute.ca/mp3/76f26519-a74c-47d8-b294-86691eea5a2d.mp3 Science http://streamer.perimeterinstitute.ca/mp3/76f26519-a74c-47d8-b294-86691eea5a2d.mp3 Wed, 01 Sep 2010 16:00:00 -0400 We study a Hamiltonian system describing a three-spin 1/2 cluster like interaction competing with an Ising-like exchange. We show that a cluster state, the ground state of the Hamiltonian in the absence of the Ising term, is provided by a hidden order of topological nature. In the presence of the cluster and Ising couplings, a continuous quantum phase transition occurs in the system, directly connecting a local broken symmetry phase to a cluster phase with the hidden order. At the critical point the Hamiltonian is self-dual. We analyze the geometric entanglement and demonstrate that it can capture the transition, as a single parameter. Luigi Amico http://streamer.perimeterinstitute.ca/mp3/a8043ce9-0bbe-4b8b-a6c4-191231c3b249.mp3 Science http://streamer.perimeterinstitute.ca/mp3/a8043ce9-0bbe-4b8b-a6c4-191231c3b249.mp3 Wed, 15 Sep 2010 16:00:00 -0400 Over the last twenty years, quantum information and quantum computing have profoundly shaped our thinking about the basic concepts of quantum physics. But can these insights also shape the way we /teach/ quantum mechanics to undergraduate physics students? A recent adventure in textbook-writing suggests some strategies and dilemmas. Ben Schumacher http://streamer.perimeterinstitute.ca/mp3/45734ad3-8620-4299-a760-b09a3196ef68.mp3 Science http://streamer.perimeterinstitute.ca/mp3/45734ad3-8620-4299-a760-b09a3196ef68.mp3 Wed, 29 Sep 2010 16:00:00 -0400 We introduce a family of variational ansatz states for chains of anyons which optimally exploits the structure of the anyonic Hilbert space. This ansatz is the natural analog of the multi-scale entanglement renormalization ansatz for spin chains. In particular, it has the same interpretation as a coarse-graining procedure and is expected to accurately describe critical systems with algebraically decaying correlations. We numerically investigate the validity of this ansatz using the anyonic golden chain and its relatives as a testbed. This demonstrates the power of entanglement renormalization in a setting with non-abelian exchange statistics, extending previous work on qudits, bosons and fermions in two dimensions. This is joint work with Ersen Bilgin. Robert Koenig http://streamer.perimeterinstitute.ca/mp3/e5ce3460-948b-4f25-9ad3-3cc0cdc531d5.mp3 Science http://streamer.perimeterinstitute.ca/mp3/e5ce3460-948b-4f25-9ad3-3cc0cdc531d5.mp3 Wed, 13 Oct 2010 16:00:00 -0400 Even though the security of quantum key distribution has been rigorously proven, most practical schemes can be attacked and broken. These attacks make use of imperfections of the physical devices used for their implementation. Since current security proofs assume that the physical devices' exact and complete specification is known, they do not hold for this scenario. The goal of device-independent quantum key distribution is to show security without making any assumptions about the internal working of the devices. In this talk, I will first explain the assumptions 'traditional' security proofs make and why they are problematic. Then, I will discuss how the violation of Bell inequalities can be used to show security even when a large part of the physical devices is untrusted. Esther Hanggi http://streamer.perimeterinstitute.ca/mp3/a1f02120-75cd-4bad-a243-1b5d121dad7e.mp3 Science http://streamer.perimeterinstitute.ca/mp3/a1f02120-75cd-4bad-a243-1b5d121dad7e.mp3 Mon, 25 Oct 2010 16:00:00 -0400 Quantum computers have emerged as the natural architecture to study the physics of strongly correlated many-body quantum systems, thus providing a major new impetus to the field of many-body quantum physics. While the method of choice for simulating classical many-body systems has long since been the ubiquitous Monte Carlo method, the formulation of a generalization of this method to the quantum regime has been impeded by the fundamental peculiarities of quantum mechanics, including, interference effects and the no-cloning theorem. We overcome those difficulties by constructing a quantum algorithm to sample from the Gibbs distribution of a quantum Hamiltonian at arbitrary temperatures, both for bosonic and fermionic systems. This is a further step in validating the quantum computer as a full quantum simulator, with a wealth of possible applications to quantum chemistry, condensed matter physics and high energy physics. Kristan Temme http://streamer.perimeterinstitute.ca/mp3/3e5d720f-6684-478b-acc6-265accd34d16.mp3 Science http://streamer.perimeterinstitute.ca/mp3/3e5d720f-6684-478b-acc6-265accd34d16.mp3 Wed, 10 Nov 2010 16:00:00 -0500 I'll describe a connection between uncertainty relations, information locking and low-distortion embeddings of L2 into L1. Exploiting this connection leads to the first explicit construction of entropic uncertainty relations for a number of measurements that is polylogarithmic in the dimension d while achieving an average measurement entropy of (1-e) log d for arbitrarily small e. From there, it is straightforward to obtain the first strong information locking scheme that is efficiently computable using a quantum computer. This locking scheme can be interpreted as a method for encrypting classical messages using a key of size much smaller than the message length. Other applications include efficient encodings for amortized quantum identification over classical channels and new string commitment protocols. Patrick Hayden http://streamer.perimeterinstitute.ca/mp3/c4aedd8c-81a0-44e2-8b33-325db9224563.mp3 Science http://streamer.perimeterinstitute.ca/mp3/c4aedd8c-81a0-44e2-8b33-325db9224563.mp3 Wed, 24 Nov 2010 16:00:00 -0500 Quantum Mechanics has been shown to provide a rigorous foundation for Statistical Mechanics. Concentration of measure, or typicality, is the main tool to construct a purely quantum derivation for the methods of Statistical Mechanics. From this point of view statistical ensembles are effective description for isolated quantum systems, since typically a random pure state of the system will have properties similar to those of the ensemble. Nevertheless, it is often argued that most of the states of the Hilbert space are not relevant for realistic systems. This talk will address this issue, presenting recent results on the emergence of typicality in the context of matrix product states, a set of physically and computationally relevant states associated to many-body Hamiltonians. Silvano Garnerone http://streamer.perimeterinstitute.ca/mp3/984e76a6-61a9-436a-9e6f-1142d86b3917.mp3 Science http://streamer.perimeterinstitute.ca/mp3/984e76a6-61a9-436a-9e6f-1142d86b3917.mp3 Wed, 02 Feb 2011 16:00:00 -0500 It is well known that the ground state energy of many-particle Hamiltonians involving only 2- body interactions can be obtained using constrained optimizations over density matrices which arise from reducing an N-particle state. While determining which 2-particle density matrices are 'N-representable' is a computationally hard problem, all known extreme N-representable 2-particle reduced density matrices arise from a unique N-particle pre-image, satisfying a conjecture established in 1972. We present explicit counterexamples to this conjecture through giving Hamiltonians with 2-body interactions which have degenerate ground states that cannot be distinguished by any 2-body operator. We relate the existence of such counterexamples to quantum error correction codes and topologically ordered spin systems. Sam Ocko http://streamer.perimeterinstitute.ca/mp3/01ee2818-20a9-414e-a2c4-c189c27f3c42.mp3 Science http://streamer.perimeterinstitute.ca/mp3/01ee2818-20a9-414e-a2c4-c189c27f3c42.mp3 Wed, 16 Feb 2011 16:00:00 -0500 For quantum fields with m=0, it is pointed out that timelike separated fields are quantized as independent subsystems. This allows us to ask the question of whether the field in the future region is entangled with the field in the past region of Minkowski space, in the Minkowski vacuum state. I will show that the answer is "yes," and then explore some consequences, including a thermal effect and a procedure for extracting the timelike entanglement with two inertial Unruh-DeWitt detectors. Stephan 'Jay' Olson http://streamer.perimeterinstitute.ca/mp3/33c20141-47a5-495e-8f90-7862fc51dbc0.mp3 Science http://streamer.perimeterinstitute.ca/mp3/33c20141-47a5-495e-8f90-7862fc51dbc0.mp3 Thu, 03 Mar 2011 16:00:00 -0500 We propose a mechanism where high entanglement between very distant boundary spins is generated by suddenly connecting two long Kondo spin chains. We show that this procedure provides an efficient way to route entanglement between multiple distant sites useful for quantum computation and multi-party quantum communication. We observe that the key features of the entanglement dynamics of the composite spin chain are remarkably well described using a simple model of two singlets, each formed by two spins. The proposed entanglement routing mechanism is a footprint of the emergence of a Kondo cloud in a Kondo system and can be engineered and observed in varied physical settings. Pasquale Sodano http://streamer.perimeterinstitute.ca/mp3/6755ec7b-f90c-46ea-8fa0-5287861b1c6d.mp3 Science http://streamer.perimeterinstitute.ca/mp3/6755ec7b-f90c-46ea-8fa0-5287861b1c6d.mp3 Wed, 16 Mar 2011 16:00:00 -0400 Two-party Bell correlation inequalities (that is, inequalities involving only correlations between dichotomic observables at each site, such as the CHSH inequality) are well-understood: Grothendieck's inequality stipulates that the quantum bias can only be a constant factor larger than the classical bias, and the maximally entangled state is always the most nonlocal resource. In part due to the complex nature of multipartite entanglement, tripartite inequalities are much more unwieldy. In a recent breakthrough result, Perez-Garcia et. al. (quant-ph/0702189) showed using tools originating from the study of operator algebras that in this setting the quantum-classical violation could be arbitrarily large. Moreover, they showed that GHZ states could only lead to bounded violations, so that they were not the most non-local states. We extend and simplify their results in a number of ways: - We show that large families of states, including generalizations of GHZ states and stabilizer states, can only lead to bounded violations. - We prove bounds on the maximal quantum-classical violation as a function both of the local dimension (this was already shown in Perez-Garcia et. al., but we give a much simpler proof), and of the number of settings per site. - We provide a simple probabilistic construction of an inequality for which there is an unbounded quantum-classical gap. Our construction is simpler, and has better parameters, than the one in Perez-Garcia et.al. It is essentially optimal in terms of the local dimension of one of the parties, and off by a quadratic factor in terms of the number of settings. In this talk I will survey some of these results, focusing on the tools that have so far been useful for their analysis (and do not involve operator algebras!). Based on joint works with Jop Briet, Harry Buhrman, and Troy Lee. Some of this work is available at arXiv:0911.4007. Thomas Vidick http://streamer.perimeterinstitute.ca/mp3/86c9c150-975f-43d9-bc55-710922d89101.mp3 Science http://streamer.perimeterinstitute.ca/mp3/86c9c150-975f-43d9-bc55-710922d89101.mp3 Wed, 30 Mar 2011 16:00:00 -0400 In many physical scenarios, close relations between the bulk properties of quantum systems and theories associated to their boundaries have been observed. In this work, we provide an exact duality mapping between the bulk of a quantum spin system and its boundary using Projected Entangled Pair States (PEPS). This duality associates to every region a Hamiltonian on its boundary, in such a way that the entanglement spectrum of the bulk corresponds to the excitation spectrum of the boundary Hamiltonian. We study various specific models, like a deformed AKLT , an Ising-type , and Kitaev's toric code, both in finite ladders and infinite square lattices. In the latter case, some of those models display quantum phase transitions. We find that a gapped bulk phase with local order corresponds to a boundary Hamiltonian with local interactions, whereas critical behavior in the bulk is reflected on a diverging interaction length of the boundary Hamiltonian. Furthermore, topologically ordered states yield non-local Hamiltonians. As our duality also associates a boundary operator to any operator in the bulk, it in fact provides a full holographic framework for the study of quantum many-body systems via their boundary. Work done in collaboration with Didier Poilblanc, Norbert Schuch, and Frank Verstraete. Ignacio Cirac http://streamer.perimeterinstitute.ca/mp3/8cac8056-7e54-42e8-b594-1dfa4927db62.mp3 Science http://streamer.perimeterinstitute.ca/mp3/8cac8056-7e54-42e8-b594-1dfa4927db62.mp3 Wed, 13 Apr 2011 16:00:00 -0400 One of the key features of the quantum Hall effect (QHE) is the fractional charge and statistics of quasiparticles. Fractionally charged anyons accumulate non-trivial phases when they encircle each other. In some QHE systems an unusual type of particles, called non-Abelian anyons, is expected to exist. When one non-Abelian particle makes a circle around another anyon this changes not only the phase but even the direction of the quantum-state vector in the Hilbert space. This property makes non-Abelian anyons promising for fault-tolerant quantum computation. Several experiments allowed an observation of fractional charges. Probing exchange statistics is more difficult and has not been accomplished for identical anyons so far. We will discuss how the statistics can be probed with Mach-Zehnder interferometry, tunneling experiments and far-from-equilibrium fluctuation-dissipation theorem. Dmitri Feldman http://streamer.perimeterinstitute.ca/mp3/4cdb5e04-8a81-4713-8a31-ce9ac366a4a1.mp3 Science http://streamer.perimeterinstitute.ca/mp3/4cdb5e04-8a81-4713-8a31-ce9ac366a4a1.mp3 Wed, 27 Apr 2011 16:00:00 -0400 This talk presents sufficient conditions for equilibration and thermalization of subsystems within closed many body quantum systems. That is, we identify when the local properties of the equilibrium state resemble those of a thermal state. With this aim, the recent progress in this field is reviewed and we introduce a novel perturbation technique for a realistic weak coupling between the subsystem and its environment. Unlike the standard perturbation theory, our technique is robust in the thermodynamic limit. Based on our thermalization results, we construct a simple and fully general quantum algorithm for preparing Gibbs states with a certified runtime and error bonds. Arnau Riera http://streamer.perimeterinstitute.ca/mp3/65900376-cc92-447b-9758-7d2c43124a5c.mp3 Science http://streamer.perimeterinstitute.ca/mp3/65900376-cc92-447b-9758-7d2c43124a5c.mp3 Wed, 18 May 2011 16:00:00 -0400 Continuous-variable SICPOVMS seem unlikely to exist, for a variety of reasons. But that doesn't rule out the possibility of other 2-designs for the continuous-variable Hilbert space L2(R). In particular, it would be nice if the coherent states -- which form a rather nice 1-design -- could be generalized in some way to get a 2-design comprising *Gaussian* states. So the question is: "Can we build a 2-design out of Gaussian states?". The answer is "No, but in a very surprising way!" Like coherent states, Gaussian states have a natural transitive symmetry group. For coherent states, it's the Heisenberg group. For Gaussian states, it's the affine symplectic group -- the Heisenberg group plus squeezings and rotations. And this group acts irreducibly on the symmetric subspace of L2(R) x L2(R)... which, by Schur's Lemma, implies that the Gaussian states *should* be a 2-design. Yet a very simple explicit calculation shows that they are not! The resolution is fascinating -- it turns out that the "symplectic twirl" involves an integral that does not quite converge, and this provides a loophole out of Schur's Lemma. So, in the end, we: (1) Show that Gaussian 2-designs do not exist, (2) Demonstrate a major stumbling block to *any* symplectic-covariant 2-designs for L2(R), (3) Gain a pretty complete understanding of *one* of the [formerly] mysterious discrepancies between discrete and continuous Hilbert spaces. Robin Blume-Kohout http://streamer.perimeterinstitute.ca/mp3/b05d38c6-2bd5-41bb-b25b-ea48117f0551.mp3 Science http://streamer.perimeterinstitute.ca/mp3/b05d38c6-2bd5-41bb-b25b-ea48117f0551.mp3 Mon, 18 Jul 2011 16:00:00 -0400 We construct a class of entangled supersymmetric states which is used as a non-local resource in the CHSH game. This class of super entangled states is more non-local then maximally entangled states if the supersymmetric degrees of freedom are accessible to measurement. Consequently, we show that the winning probability for the CHSH game is greater than cos2(pi/8) corresponding to an expected value greater than Tsirelson's bound. Kamil Bradler http://streamer2.perimeterinstitute.ca/mp3/11100050.mp3 Science http://streamer2.perimeterinstitute.ca/mp3/11100050.mp3 Wed, 12 Oct 2011 16:00:00 -0400 We provide a microscopic understanding of the nucleation of topological quantum liquids that arise due to interactions between non-Abelian anyons. With the pairwise anyon interactions typically showing RKKY-type oscillations in sign, but decaying exponentially with distance, we show that the character of the nucleated phase is fully determined by anyon interactions beyond nearest neighbor exchange. We investigate this issue in the context of Kitaev's honeycomb lattice model. In the presence of vortex lattices, depending on microscopic parameters such as the vortex lattice spacing, we observe the nucleation of several distinct Abelian topological phases, that differ in their band structure and Chern number description. By employing an effective model of Majorana fermions, we show that these phases can be fully predicted from the vortex-vortex interactions. Corresponding microscopic results should hold for vortices forming an Abrikosov lattice in a p-wave superconductor or quasiholes forming a Wigner crystal in non-Abelian quantum Hall states. Ville Lahtinen http://streamer2.perimeterinstitute.ca/mp3/11100074.mp3 Science http://streamer2.perimeterinstitute.ca/mp3/11100074.mp3 Wed, 26 Oct 2011 16:00:00 -0400 I will first present a theorem based on the Decoupling Theorem of [1] which gives sufficient and necessary conditions for a quantum channel (CPTPM) being such that it yields the same output for almost all possible inputs. This theorem allows us to reproduce and generalize results oft [2,3], in which cornerstones of statistical physics are derived from first principles of quantum mechanics, in a very natural and easy way. Specifically, we express them in a way which allows to apply results about random 2-qubit interactions [4]. Furthermore, we apply this theorem to provide a criterion for whether different initial states of some subspace of a quantum mechanical system in contact with an environment have at some given time already evolved to the same state or not. As it turns out, this question can be answered by examining a simple entropic inequality evaluated for just one particular state [5]. Applying this criterion to realistic Hamiltonians with local interactions may lead to improved bounds on the thermalization times of quantum mechanical systems. Adrian Hutter http://streamer2.perimeterinstitute.ca/mp3/12010120.mp3 Science http://streamer2.perimeterinstitute.ca/mp3/12010120.mp3 Wed, 25 Jan 2012 16:00:00 -0500