This series consists of talks in the area of Foundations of Quantum Theory. http://pirsa.org/podcast/S002 Science 2012 http://blogs.law.harvard.edu/tech/rss en-ca Thu, 09 Feb 2012 04:24:02 -0500 sbradwell@perimeterinstitute.ca Thu, 09 Feb 2012 04:24:02 -0500 G 180 sbradwell@perimeterinstitute.ca Steve Bradwell's - Podcast Generator Howard Wiseman http://streamer.perimeterinstitute.ca/mp3/867319c6-5a88-4c07-8187-c6145f3529ff.mp3 Science http://streamer.perimeterinstitute.ca/mp3/867319c6-5a88-4c07-8187-c6145f3529ff.mp3 Thu, 14 Oct 2004 16:05:00 -0400 Alexei Grinbaum http://streamer.perimeterinstitute.ca/mp3/d161ce68-8607-4c91-957d-7d81f9f47285.mp3 Science http://streamer.perimeterinstitute.ca/mp3/d161ce68-8607-4c91-957d-7d81f9f47285.mp3 Thu, 10 Feb 2005 11:30:00 -0500 Natural critical phenomena are characterized by laminar periods separated by events where bursts of activity take place, and by the interrelated self-similarity of space-time scales and of the event sizes. One example are earthquakes: for this case a new approach to quantify correlations between events reveals new phenomenology. By linking correlated earthquakes one creates a scale-free network of events, which can have applications in hazard assessment. Solar flares are another example of critical phenomenon, where event sizes and time scales are part of a single self-similar scenario: rescaling time by the rate of events with intensity greater than an intensity threshold, the waiting time distributions conform to scaling functions that are independent of the threshold. The concept of self-organized criticality (SOC) is suitable to describe critical phenomena, but we highlight problems with most of the classical models of SOC (usually called sandpiles) to fully capture the space-time complexity of real systems. In order to fix this shortcoming, we put forward a strategy giving good results when applied to the simplest sandpile models. Marco Blaiesi http://streamer.perimeterinstitute.ca/mp3/69ca696e-f5f8-4a21-8e0b-3567a6203131.mp3 Science http://streamer.perimeterinstitute.ca/mp3/69ca696e-f5f8-4a21-8e0b-3567a6203131.mp3 Thu, 14 Apr 2005 14:00:00 -0400 The problem of associating beables (hidden variables) to QFT, in the spirit of what Bohm did for nonrelativistic QM, is not trivial. In 1984, John Bell suggested a way of solving the problem, according to which the beables are the positions of fermions, in a discretized version of QFT, and obey a stochastic evolution that simulates all predictions of QFT. In the continuum limit, it will be shown that the Bell model becomes deterministic and that it is related to the choice of the charge density as a beable. Moreover, the charge superselection rule is a consequence of the Bell model. The non-relativistic limit and the derivation of Bohm's first quantized interpretation in this limit are also studied. I will also consider whether the Bell model can be applied to bosons. Samuel Colin http://streamer.perimeterinstitute.ca/mp3/37e98831-574d-43a8-a36b-72f2f194a0b2.mp3 Science http://streamer.perimeterinstitute.ca/mp3/37e98831-574d-43a8-a36b-72f2f194a0b2.mp3 Tue, 31 Jan 2006 16:00:38 -0500 We will postulate a novel notion of probability; this will involve introducing an extra axiom of probability that seems natural from a Bayesian perspective. We will then provide an analogue of Gleason's theorem for these probabilities. We will also discuss why this approach may be useful for generalizations of quantum theory such as quantum gravity theories; this will involve discussing an analogy between Bayesian approaches and relational approaches. Thomas Marlow http://streamer.perimeterinstitute.ca/mp3/ffd9e2c7-50fc-47e0-953f-9afd2d7eb305.mp3 Science http://streamer.perimeterinstitute.ca/mp3/ffd9e2c7-50fc-47e0-953f-9afd2d7eb305.mp3 Tue, 14 Feb 2006 16:00:50 -0500 Collapse models are one of the most promising attempts to overcome the measurement problem of quanum mechanics: they descibe, within one single framework, both the quantum properties of microscopic systems and the classical properties of macroscopic objects, and in particular they explain why measurements always have definite outcomes, distributed according to the Born probability rule. We will discuss some recent developments in this field: i) we will show how it is possible to formulate collapse models in such a way that the mean energy of physical system does non increse indefinitely, a typical feature of the models first proposed in the literature; ii) we will discuss recent experiments aiming at testing the validity of the superposition principle, thus of collapse models, at the mesoscopic level. Emiliano Ippoliti http://streamer.perimeterinstitute.ca/mp3/0bb3931c-9a45-49f8-be23-98c71fb5dca8.mp3 Science http://streamer.perimeterinstitute.ca/mp3/0bb3931c-9a45-49f8-be23-98c71fb5dca8.mp3 Mon, 20 Feb 2006 14:00:29 -0500 The mathematical formalism of quantum theory has many features whose physical origin remains obscure. In this paper, we attempt to systematically investigate the possibility that the concept of information may play a key role in understanding some of these features. We formulate a set of assumptions, based on generalizations of experimental facts that are representative of quantum phenomena and physically comprehensible theoretical ideas and principles, and show that it is possible to deduce the finite-dimensional quantum formalism from these assumptions. The concept of information, via an information-theoretic invariance principle, plays a central role in the derivation, and gives rise to some of the central structural features of the quantum formalism. Philip Goyal http://streamer.perimeterinstitute.ca/mp3/b2e89d35-a583-4ba1-8c6a-996ebd55bb26.mp3 Science http://streamer.perimeterinstitute.ca/mp3/b2e89d35-a583-4ba1-8c6a-996ebd55bb26.mp3 Mon, 22 Jan 2007 14:00:00 -0500 Results in decoherence theory and entanglement theory will be considered as tools illuminating the foundation of quantum mechanics and the possible relationship of quantum information to it. Gregg Jaeger http://streamer.perimeterinstitute.ca/mp3/8499ba1d-e2c0-4f3d-acc7-a4bf385400d9.mp3 Science http://streamer.perimeterinstitute.ca/mp3/8499ba1d-e2c0-4f3d-acc7-a4bf385400d9.mp3 Thu, 15 Mar 2007 16:00:00 -0400 Adrian Kent http://streamer.perimeterinstitute.ca/mp3/a9424df3-e9ce-4384-86bc-95d320c0579f.mp3 Science http://streamer.perimeterinstitute.ca/mp3/a9424df3-e9ce-4384-86bc-95d320c0579f.mp3 Thu, 27 Sep 2007 16:00:00 -0400 Harvey Brown http://streamer.perimeterinstitute.ca/mp3/f738f460-7062-4d34-ac59-618ecd112c70.mp3 Science http://streamer.perimeterinstitute.ca/mp3/f738f460-7062-4d34-ac59-618ecd112c70.mp3 Tue, 16 Oct 2007 16:00:00 -0400 The solution of many problems in quantum information is critically dependent on the geometry of the space of density matrices. For a Hilbert space of dimension 2 this geometry is very simple: it is simply a sphere. However for Hilbert spaces of dimension greater than 2 the geometry is much more interesting as the bounding hypersurface is both highly symmetric (it has a d^2 real parameter symmetry group, where d is the dimension) and highly convoluted. The problem of getting a better understanding of this hypersurface is difficult (it is hard even in the case of a single qutrit). It is also, we believe, both physically important and mathematically deep. In this talk we relate the problem to MUBs (mutually unbiased bases) and SIC-POVMs (symmetric informationally complete positive operator valued measures). These structures were originally introduced in connection with tomography. However, that by no means exhausts their importance. In particular their existence (non-existence???) in a given dimension is a source of significant insight into the state space geometry in that dimension. SIC-POVMs are especially important in this regard as they provide a a natural set of coordinates for state space. In this talk we give an overview of the problem. We then go on to describe some recent results obtained in collaboration with Chris Fuchs and Hoan Dang (also see recent work by Wootters and Sussman). In particular we describe the connection with minimum uncertainty states. These states, besides being interesting in themselves (they are a kind of discrete analogue of coherent states with important cryptographic applications), suggest a potentially fruitful line of attack on the still outstanding SIC existence problem. Marcus Appleby http://streamer.perimeterinstitute.ca/mp3/81691831-fbf4-4111-ab3b-782dabeae12f.mp3 Science http://streamer.perimeterinstitute.ca/mp3/81691831-fbf4-4111-ab3b-782dabeae12f.mp3 Tue, 23 Oct 2007 16:00:00 -0400 The simplest algebraic curves of genus one are the nonsingular cubics in two-dimensional complex projective space. Interpreting CP^2 as the space of pure quantum states associated with a Hilbert space of dimension three, I will show how various properties of d=3 symmetric informationally complete positive operator valued measures can be understood in terms of the geometry of such curves. The resulting structure, although of considerable complexity, is very beautiful from a mathematical perspective. Lane Hughston http://streamer.perimeterinstitute.ca/mp3/de000ea9-d730-4972-9ad9-6f9bb630abd5.mp3 Science http://streamer.perimeterinstitute.ca/mp3/de000ea9-d730-4972-9ad9-6f9bb630abd5.mp3 Tue, 30 Oct 2007 16:00:00 -0400 What if the second law of thermodynamics, in the hierarchy of physical laws, were at the same level as the fundamental laws of mechanics, such as the great conservation principles? What if entropy were an intrinsic property of matter at the same level as energy is universally understood to be? What if irreversibility were an intrinsic feature of the microscopic dynamical law of all physical objects, including an individual qubit or qudit? This talk will show how positive answers to these questions need not contradict any of the known results of quantum mechanics. We construct a logically consistent, mathematically sound and definite, physically intriguing, non-relativistic and non-statistical quantum theory, in which the second law of thermodynamics is embedded as a fundamental microscopical law. The theory hinges upon a nonlinear extension of unitary Hamiltonian dynamics which for uncorrelated and noninteracting systems reduces to the usual Schroedinger equation for the zero entropy states, but in general generates a group (not a semi group) of irreversible time evolutions, where the non-Hamiltonian entropy generating term in the evolution equation attracts the state towards the direction of maximal entropy increase. Various examples and features of this highly non-conventional dynamical theory are discussed. References available at http://www.quantumthermodynamics.org/ Gian Paolo Beretta http://streamer.perimeterinstitute.ca/mp3/ab1be05e-5878-4494-b4e8-aa37086a137e.mp3 Science http://streamer.perimeterinstitute.ca/mp3/ab1be05e-5878-4494-b4e8-aa37086a137e.mp3 Thu, 08 Nov 2007 16:00:00 -0500 A new microcanonical equilibrium state is introduced for quantum systems with finite-dimensional state spaces. Equilibrium is characterised by a uniform distribution on a level surface of the expectation value of the Hamiltonian. The distinguishing feature of the proposed equilibrium state is that the corresponding density of states is a continuous function of the energy, and hence thermodynamic functions are well defined for finite quantum systems. The density of states, however, is not in general an analytic function. It is demonstrated that generic quantum systems therefore exhibit second-order phase transitions at finite temperatures. The talk is based on work carried out in collaboration with D.W. Hook and L.P. Hughston. Dorje Brody http://streamer.perimeterinstitute.ca/mp3/82207552-2da5-4ae9-9100-2daa2fb97797.mp3 Science http://streamer.perimeterinstitute.ca/mp3/82207552-2da5-4ae9-9100-2daa2fb97797.mp3 Tue, 13 Nov 2007 16:00:00 -0500 Several finite dimensional quasi-probability representations of quantum states have been proposed to study various problems in quantum information theory and quantum foundations. These representations are often defined only on restricted dimensions and their physical significance in contexts such as drawing quantum-classical comparisons is limited by the non-uniqueness of the particular representation. Here we show how the mathematical theory of frames provides a unified formalism which accommodates all known quasi-probability representations of finite dimensional quantum systems. Chris Ferrie http://streamer.perimeterinstitute.ca/mp3/e17ce84c-8c7e-47aa-a48e-565879150d49.mp3 Science http://streamer.perimeterinstitute.ca/mp3/e17ce84c-8c7e-47aa-a48e-565879150d49.mp3 Tue, 20 Nov 2007 16:00:00 -0500 We derive a set of Bell inequalities using correlated random variables. Our inequalities are necessary conditions for the existence of a local realistic description of projective measurements on qubits. We analyze our inequalities for the case of two qubits and find that they are equivalent to the well known CHSH inequalities. We also discuss the sufficiency of our inequalities as well as their applicability to more than two qubits. Matt Elliott http://streamer.perimeterinstitute.ca/mp3/177d7373-86de-40c8-9ffa-e06e22480986.mp3 Science http://streamer.perimeterinstitute.ca/mp3/177d7373-86de-40c8-9ffa-e06e22480986.mp3 Tue, 27 Nov 2007 16:00:00 -0500 In any attempt to construct a Quantum Theory of Gravity, one has to deal with the fact that Time in Quantum Mechanics appears to be very different from Time in General Relativity. This is the famous (or actually notorious!) "Problem of Time", and gives rise to both conceptual and technical problems. The decoherent histories approach to quantum theory, is an alternative formulation of quantum theory specially designed to deal with closed (no-external observer or environment) systems. This approach has been considered particularly promising, in dealing with the problem of time, since it puts space and time in equal footing (unlike standard QM) . This talk develops a particular implementation of the above expectations, i.e. we construct a general set of "Class Operators" corresponding to questions that appear to be "Timeless" (independent of the parameter time), but correspond to physically interesting questions. This is similar to finding a general enough set of timeless observables, in the evolving constants approach to the problem of time. Petros Wallden http://streamer.perimeterinstitute.ca/mp3/adf4942f-05d3-4ad4-bf0b-f9792389d52a.mp3 Science http://streamer.perimeterinstitute.ca/mp3/adf4942f-05d3-4ad4-bf0b-f9792389d52a.mp3 Tue, 11 Dec 2007 16:00:00 -0500 Bell\'s theorem is commonly understood to show that EPR correlations are not explainable via a local hidden variable theory. But Bell\'s theorem assumes that the initial state of the particles is independent of the final detector settings. It has been proposed that this independence assumption might be undermined by a relativistically-allowed form of \"backward causation\", thereby allowing construction of a local hidden-variable model after all. In this talk, I will show that there is no backward causation model which yields the desired correlations. However, there are other physical scenarios yielding nontrivial nonlocal correlations which violated Bell\'s independence assumption. I will present two. Steve Weinstein http://streamer.perimeterinstitute.ca/mp3/4586fbbc-8249-4646-8eb1-1d62693ab30a.mp3 Science http://streamer.perimeterinstitute.ca/mp3/4586fbbc-8249-4646-8eb1-1d62693ab30a.mp3 Tue, 15 Jan 2008 16:00:00 -0500 Mutually unbiased bases (MUBs) have attracted a lot of attention the last years. These bases are interesting for their potential use within quantum information processing and when trying to understand quantum state space. A central question is if there exists complete sets of N+1 MUBs in N-dimensional Hilbert space, as these are desired for quantum state tomography. Despite a lot of effort they are only known in prime power dimensions. I will describe in geometrical terms how a complete set of MUBs would sit in the set of density matrices and present a distance between bases–a measure of unbiasedness. Then I will explain the relation between MUBs and Hadamard matrices, and report on a search for MUB-sets in dimension N=6. In this case no sets of more than three MUBs are found, but there are several inequivalent triplets. Asa Ericsson http://streamer.perimeterinstitute.ca/mp3/129a237b-d52b-4f01-840d-580317f875d2.mp3 Science http://streamer.perimeterinstitute.ca/mp3/129a237b-d52b-4f01-840d-580317f875d2.mp3 Tue, 12 Feb 2008 16:00:00 -0500 The purpose of this talk is to describe bosonic fields and their Lagrangians in the causal set context. Spin-0 fields are defined to be real-valued functions on a causal set. Gauge fields are viewed as SU(n)-valued functions on the set of pairs of elements of a causal set, and gravity is viewed as the causal relation itself. The purpose of this talk is to come up with expressions for the Lagrangian densities of these fields in such a way that they approximate the Lagrangian densities expected from regular Quantum Field Theory on a differentiable manifold in the special case where the causal set is a random sprinkling of points in the manifold. I will then conjecture that that same expression is appropriate for an arbitrary causal set. Roman Sverdlov http://streamer.perimeterinstitute.ca/mp3/a9485b59-130e-4c06-8a7d-b5bcd6c3b786.mp3 Science http://streamer.perimeterinstitute.ca/mp3/a9485b59-130e-4c06-8a7d-b5bcd6c3b786.mp3 Tue, 19 Feb 2008 16:00:00 -0500 We prove that all non-conspiratorial/retro-causal hidden variable theories has to be measurement ordering contextual, i.e. there exists *commuting* operator pair (A,B) and a hidden state \\lambda such that the outcome of A depends on whether we measure B before or after. Interestingly this rules out a recent proposal for a psi-epistemic due to Barrett, Hardy, and Spekkens. We also show that the model was in fact partly discovered already by vanFraassen 1973; the only thing missing was giving a probability distribution on the space of ontic states (the hidden variables). Hans Westman http://streamer.perimeterinstitute.ca/mp3/1e4f63a2-d0da-4484-84d5-1dd0e634bca2.mp3 Science http://streamer.perimeterinstitute.ca/mp3/1e4f63a2-d0da-4484-84d5-1dd0e634bca2.mp3 Tue, 26 Feb 2008 16:00:00 -0500 A single classical system is characterized by its manifold of states; and to combine several systems, we take the product of manifolds. A single quantum system is characterized by its Hilbert space of states; and to combine several systems, we take the tensor product of Hilbert spaces. But what if we choose to combine an infinite number of systems? A naive attempt to describe such combinations fails, for there is apparently no natural notion of an infinite product of manifolds; nor of an infinite tensor product of Hilbert spaces. But, at least in the quantum case, the situation is not as hopeless as it might appear. We argue that there does indeed exist a natural mathematical framework for combinations of infinite numbers of quantum systems. Robert Geroch http://streamer.perimeterinstitute.ca/mp3/ed9ec9f4-d8c9-4d9e-aeb6-691bcc52ecc9.mp3 Science http://streamer.perimeterinstitute.ca/mp3/ed9ec9f4-d8c9-4d9e-aeb6-691bcc52ecc9.mp3 Thu, 13 Mar 2008 11:00:00 -0400 It is usually expected that nonrelativistic many-body Schroedinger equations emerge from some QFT models in the limit of infinite masses. For instance, from Yukawa's QFT, if the initial state contains 2 fermions, we expect to recover a 2-fermion nonrelativistic Schroedinger equation with 2-body Yukawa potential (in the limit of infinite fermion mass). I will give an easy (but still heuristic) derivation of this, based on the analysis of the corresponding Feynman diagrams and on the behaviour of the complete propagators for large spacetime distances. Then, I may outline another possible derivation based on the Schroedinger picture and dressed particles. Samuel Colin http://streamer.perimeterinstitute.ca/mp3/10a99636-77fa-430d-b802-7ec035112b78.mp3 Science http://streamer.perimeterinstitute.ca/mp3/10a99636-77fa-430d-b802-7ec035112b78.mp3 Tue, 18 Mar 2008 16:00:00 -0400 Quantum measure theory describes quantum theory as a generalization of a classical stochastic process, which may be fruitful for quantum gravity. I will describe the approach, and show that, in the context of an EPRB setup with two distant experimenters, two alternative experiments, and two outcomes per experiment, any set of no signaling probabilities can be realized, albeit by violating a `strong positivity' condition. David Rideout http://streamer.perimeterinstitute.ca/mp3/faf0a8ad-e988-4eba-ba2c-b6a62baa4125.mp3 Science http://streamer.perimeterinstitute.ca/mp3/faf0a8ad-e988-4eba-ba2c-b6a62baa4125.mp3 Tue, 01 Apr 2008 16:00:00 -0400 Chris Isham in pre-recorded video, with Andreas Doring fielding questions and clarifications. Like watching commentators Scott Hamilton and Katarina Witt analyze Kristi Yamaguchi's performance at the World Figure Skating Championships for CBS News, join us for something different in quantum foundations. Chris Isham parries the intricacies of topos theory; Andreas Doring shows us how to see the moves in slow motion. Bring your own popcorn and plenty of questions. Andreas Doering http://streamer.perimeterinstitute.ca/mp3/c437305e-e0e6-4364-8202-c4087d9b0aec.mp3 Science http://streamer.perimeterinstitute.ca/mp3/c437305e-e0e6-4364-8202-c4087d9b0aec.mp3 Tue, 08 Apr 2008 16:00:00 -0400 The dynamics of particles moving in a medium defined by its relativistically invariant stochastic properties is investigated. For this aim, the force exerted on the particles by the medium is defined by a stationary random variable as a function of the proper time of the particles. The equations of motion for a single one-dimensional particle are obtained and numerically solved. A conservation law for the drift momentum of the particle during its random motion is shown. Moreover, the conservation of the mean value of the total linear momentum for two particles repelling each other according to the Coulomb interaction also follows. Therefore, the results indicate the realization of a kind of stochastic Noether theorem in the system under study. Alejandro Cabo http://streamer.perimeterinstitute.ca/mp3/10929e8a-b9d1-4f77-a1b8-533518c8b2c8.mp3 Science http://streamer.perimeterinstitute.ca/mp3/10929e8a-b9d1-4f77-a1b8-533518c8b2c8.mp3 Tue, 22 Apr 2008 16:00:00 -0400 Consider the quantum predictions for EPR-type measurements on two systems with Hilbert space of dimension at least 3 in any maximally entangled state. I show that the only possible hidden variables model of these probabilities that satisfies both Shimony's and Jarrett's condition of parameter independence (or `locality') and Jones and Clifton's condition of conditional parameter independence (or `constrained locality') is trivial, i.e. given by the quantum probabilities themselves. I shall attempt to discuss also the meaning of the conditions and of this result. Guido Bacciagaluppi http://streamer.perimeterinstitute.ca/mp3/1b654c76-a4ed-4ff1-ba07-07013f3cd0cc.mp3 Science http://streamer.perimeterinstitute.ca/mp3/1b654c76-a4ed-4ff1-ba07-07013f3cd0cc.mp3 Tue, 29 Apr 2008 16:00:00 -0400 Shih-Yuin Lin http://streamer.perimeterinstitute.ca/mp3/1616ed7a-e037-490a-8e8e-ff0def89869c.mp3 Science http://streamer.perimeterinstitute.ca/mp3/1616ed7a-e037-490a-8e8e-ff0def89869c.mp3 Tue, 06 May 2008 16:00:00 -0400 Some theoretical physicists, Chris Fuchs among them, take quantum mechanics to go hand in hand with an anti-representationalist account of truth and reality such as that offered by the American pragmatists - William James, Charles Peirce, Richard Rorty, etc. On this view, scientific theories are instruments, rather than mirrors of the real world. In this talk, I’ll suggest that if the quantum physicist is to team up with the pragmatist, he’d do best to join not with James and Rorty, who see the world as radically plastic or malleable. He would do best to join with the founder of pragmatism, Peirce, who argued that a regulative assumption of inquiry is that there is a right or determinate answer to the question at hand. It may look as if the anti-representationalist quantum theorist will be unhappy with this suggestion, but I’ll argue that this would be a mistake. The trail of the human serpent, as James said, is over everything but, as Peirce saw, this does not toss us into the sea of post-modern arbitrariness, where there is nothing to say about what is true and what is real. Cheryl Misak http://streamer.perimeterinstitute.ca/mp3/61516ff6-a838-42d4-8a05-474d0839defa.mp3 Science http://streamer.perimeterinstitute.ca/mp3/61516ff6-a838-42d4-8a05-474d0839defa.mp3 Tue, 20 May 2008 16:00:00 -0400 The focus of this talk is a particular feature of the statistical behavior of elementary particles, simple composite systems of them and the quantum probability theory to which this behavior gives rise. The standard interpretation of a generalized probability theory of the sort found in quantum mechanics is that its probabilities are probabilities of propositions belonging to particles, where a proposition belongs to a particle if its constituent dynamical property is a possible property of the particle. The feature of interest is the fact that there exist simple systems and finite combinations of propositions belonging to them for which no two-valued measures are possible. I will argue that quantum probabilities are not satisfactorily interpretable as probabilities of propositions belonging to particles, and that such an interpretation is possible only when the propositions to which probabilities are assigned form (an algebraic structure which is homomorphic to) a Boolean algebra. The idea I will develop is that the probabilities of quantum mechanics are probabilities of “effects,” probabilities of the traces of particleinteractions with objects and processes that are epistemically accessible to us. I hope to make it clear that such a view is not committed to any kind of anti-realism about the micro-world, that its mildly instrumentalist flavor is not a defect but a strength, and that it illuminates at least one otherwise paradoxical feature of quantum mechanics. William Demopoulos http://streamer.perimeterinstitute.ca/mp3/2ea7f711-9285-4fd1-a59a-8e7391e26d65.mp3 Science http://streamer.perimeterinstitute.ca/mp3/2ea7f711-9285-4fd1-a59a-8e7391e26d65.mp3 Tue, 27 May 2008 16:00:00 -0400 TBA Daniel Parker http://streamer.perimeterinstitute.ca/mp3/2a4080f3-2a23-470f-a278-4988e6266339.mp3 Science http://streamer.perimeterinstitute.ca/mp3/2a4080f3-2a23-470f-a278-4988e6266339.mp3 Thu, 29 May 2008 16:00:00 -0400 It is well known that the derivation of the Bell Inequality rests on two major assumptions, usually called outcome independence and parameter independence. Parameter independence seems to have a straightforward motivation: it expresses a non-signalling requirement between space-like separated sites and is thus motivated by locality. The status of outcome independence is much les clear. Many authors have argued that this assumption too expresses a locality requirement, in the form of a 'screening off' condition. I will argue that the assumption also admits of an entirely different interpretation, suggested by the concept of sufficiency in the general theory of statistical inference. In this view, the assumption of outcome independence can be explained as expressing the idea that the specification of the hidden variable is sufficient, i.e. it exhausts all the relevant statistical information about the measurement outcomes. In this view, the assumption has no roots in locality at all. Rather, I would claim, it stems from the assumption that there exists such an exhaustive state description in our putative hidden variable theories. Jos Uffink http://streamer.perimeterinstitute.ca/mp3/d732e94c-df62-41c8-aee8-76a9e155dc1d.mp3 Science http://streamer.perimeterinstitute.ca/mp3/d732e94c-df62-41c8-aee8-76a9e155dc1d.mp3 Tue, 10 Jun 2008 16:00:00 -0400 I will comment on the prevailing atmosphere and attitudes that provoked the CJS theorem, aspects of the theorem itself, some features of the aftermath following the theorem and, finally, a critique of the relevance of the theorem based on my own research on position operators in Lorentz covariant quantum theory. Gordon Fleming http://streamer.perimeterinstitute.ca/mp3/1a7787fa-5478-49ca-82c2-4b7a342117c8.mp3 Science http://streamer.perimeterinstitute.ca/mp3/1a7787fa-5478-49ca-82c2-4b7a342117c8.mp3 Tue, 17 Jun 2008 16:00:00 -0400 Set theory provides foundations of mathematics in the sense that all the mathematical notions like numbers, functions, relations, structures are defined in the axiomatic set theory called ZFC. Quantum set theory naturally extends ZFC to quantum logic. Hence, we can expect that quantum set theory provides mathematics based on quantum logic. In this talk, I will show a useful application of quantum set theory to quantum mechanics based on the fact that the real numbers constructed in quantum set theory exactly corresponds to the quantum observables. The standard formulation of quantum mechanics answers the question as to in what state an observable A has the value in an interval I. However, the question is not answered as to in what state two observables A and B have the same value. The notion of equality between the values of observables will play many important roles in foundations of quantum mechanics. The notion of measurement of an observable relies on the condition that the observable to be measured and the meter after the measurement should have the same value. We can define the notion of quantum disturbance through the condition whether the values of the given observable before and after the process is the same. It is shown that all the observational propositions on a quantum system corresponds to some propositions in quantum set theory and the equality relation naturally provides the proposition that two observables have the same value. It has been broadly accepted that we cannot speak of the values of quantum observables without assuming a hidden variable theory. However, quantum set theory enables us to do so without assuming hidden variables but alternatively under the consist use of quantum logic, which is more or less considered as logic of the superposition principle. [1] M. Ozawa, Transfer principle in quantum set theory, J. Symbolic Logic 72, 625-648 (2007), online preprint: http://arxiv.org/abs/math.LO/0604349. [2] M. Ozawa, Quantum perfect correlations, Ann. Phys. (N.Y.) 321, 744--769 (2006), online preprint: LANL quant-ph/0501081. Masanao Ozawa http://streamer.perimeterinstitute.ca/mp3/5f52bfe9-d841-45b0-b89d-bf7ab2b6dc9d.mp3 Science http://streamer.perimeterinstitute.ca/mp3/5f52bfe9-d841-45b0-b89d-bf7ab2b6dc9d.mp3 Tue, 24 Jun 2008 16:00:00 -0400 We investigate the strengths and weaknesses of the Spekkens toy model for quantum states. We axiomatize the Spekkens toy model into a set of five axioms, regarding valid states, transformations, measurements and composition of systems. We present two relaxations of the Spekkens toy model, giving rise to two variant toy theories. By relaxing the axiom regarding valid transformations a group of toy operations is obtained that is equivalent to the projective extended Clifford Group for one and two qubits. However, the physical state of affairs resulting from this relaxation is undesirable, violating the desideratum that single toy bit operations must compose under the tensor product. The second variant toy theory is obtained by relaxing the axioms regarding valid states and measurements, resulting in a toy model that exhibits the Kochen-Specker property. Like the previous toy model, the relaxation renders the toy model physically undesirable. Therefore, we claim that the Spekkens toy model is optimal; altering its axioms does not yield a better epistemic description of quantum theory. This work is a collaboration with Gilad Gour, Aidan Roy and Barry C. Sanders. Michael Skotiniotis http://streamer.perimeterinstitute.ca/mp3/00506931-3440-4b3b-9c6b-be46e70618e7.mp3 Science http://streamer.perimeterinstitute.ca/mp3/00506931-3440-4b3b-9c6b-be46e70618e7.mp3 Tue, 08 Jul 2008 16:00:00 -0400 In deBroglie-Bohm theory the quantum state plays the role of a guiding agent. In this seminar we will explore if this is a universal feature shared by all hidden variable theories or merely a peculiar feature of deBroglie-Bohm theory. We present the bare bones of a model in which the quantum state represents a probability distribution and does not act as a guiding agent. The theory is also psi-epistemic according to Spekken's and Harrigan's definition. For simplicity we develop the model for a 1D discrete lattice but the generalization to higher dimensions is straightforward. The ontic state consists of a definite particle position and in addition possible non-local links between spatially separated lattice points. These non-local links comes in two types: directed links and non-directed links. Entanglement manifests itself through these links. Interestingly, this ontology seems to be the simplest possible and immediately suggested by the structure of quantum theory itself. For N lattice points there are N*3^(N(N-1)) ontic states growing exponentially with the Hilbert space dimension N as expected. We further require that the evolution of the probability distribution on the ontic state space is dictated by a master equation with non-negative transition rates. It is then easy to show that one can reproduce the Schroedinger equation if an only if there are positive solutions to a gigantic system of linear equations. This is a highly non-trivial problem and whether there exists such positive solutions or not is still not clear to me. Alternatively one can view this set of linear equations as constraints on the possible types of Hamiltonians. We end by speculating how one might incorporate gravity into this theory by requiring permutation invariance of the dynamical evolution law. Hans Westman http://streamer.perimeterinstitute.ca/mp3/0718a5a5-8336-4e33-b0c8-93db608d66f7.mp3 Science http://streamer.perimeterinstitute.ca/mp3/0718a5a5-8336-4e33-b0c8-93db608d66f7.mp3 Tue, 22 Jul 2008 04:00:00 -0400 Domains were introduced in computer science in the late 1960's by Dana Scott to provide a semantics for the lambda calculus (the lambda calculus is the basic prototype for a functional programming language i.e. ML). The study of domains with measurements was initiated in the speaker's thesis: a domain provides a qualitative view of information expressed in part by an 'information order' and a measurement on a domain expresses a quantitative view of information with respect to the underlying qualitative aspect. The theory of domains and measurements was initially introduced to provide a first order model of computation, one in which a computation is viewed as a process that evolves in a space of informatic objects, where processes have informatic rates of change determined by the manner in which they manipulate information. There is a domain of binary channels with capacity as a measurement. There is a domain of finite probability distributions with entropy as a measurement. There is a domain of quantum mixed states with entropy as a measurement. There is a domain of spacetime intervals with global time as a measurement. In this setting, similarities between QM and GR emerge, but also some important differences. In a domain, if we write x <= y, then it means that x carries information about y, while x << y is a stronger relation that means x carries *essential* information about y. In GR, the domain theoretic relation << can be proven to be timelike causality. It possesses stronger mathematical properties than << does in QM. However, by an application of the maximum entropy principle, we can restrict the mixed states in consideration and this difference is removed: the domains of events and mixed states are both globally hyperbolic -- where globally hyperbolic is a purely order theoretic idea that just happens to coincide with the usual notion in the case of GR. Along the way, we will see domain theoretic ways of distinguishing between the Newtonian and relativistic notions of time, how to reconstruct the topology and geometry of spacetime in a purely order theoretic manner beginning from only a countable set, see that the Holevo capacity of a unital qubit channel is determined by the largest value of its informatic derivative and have reason to wonder if distance can be defined as the amount of information (capacity) that can be transmitted between two points. Keye Martin http://streamer.perimeterinstitute.ca/mp3/79f2d303-4699-426c-b318-30fecff75cc4.mp3 Science http://streamer.perimeterinstitute.ca/mp3/79f2d303-4699-426c-b318-30fecff75cc4.mp3 Tue, 12 Aug 2008 16:00:00 -0400 Theoretical and experimental results on the Quantum Injected Optical Parametric Amplification (QI-OPA) of optical qubits in the high gain regime (g &gt; 6) are reported. The entanglement of the related Schroedinger Cat-State (SCS) is demonstrated as well as the establishment of Phase-Covariant quantum cloning for a Macrostate consisting of about 106 particles. In addition, the violation of the CHSH inequality is has been realized experimentally. According to the original 1935 definition of the SCS, the overall apparatus establishes for the first time the nonlocal correlations between a microcopic spin (qubit) and a high J angular momentum i.e. a macroscopic multiparticle system close to the classical limit. Applications to Quantum Information will be discussed. Francesco De Martini http://streamer.perimeterinstitute.ca/mp3/3fd65f19-b8d5-4d0a-af9b-1cb2d8d5bd8e.mp3 Science http://streamer.perimeterinstitute.ca/mp3/3fd65f19-b8d5-4d0a-af9b-1cb2d8d5bd8e.mp3 Tue, 26 Aug 2008 16:00:00 -0400 After using the complex Hilbert space formalism for quantum theory for so long, it is very easy to begin to take for granted features like projection operators and the projection postulate, the algebra of observables, symmetric transition probabilities, linear evolution, etc.... Over the past 50 years there have been many attempts to gain a better understanding of this formalism by reconstructing it from different kinds of (sometimes) physically motivated assumptions. By looking at how the above features are motivated and used in different reconstructions, it becomes clear just how special and restrictive many of them are. The question is then what a theory which does not have some of these features looks like. Another interesting question is whether there are any reasons to be suspicious of postulating them in reconstructions or when trying to generalize or apply the quantum formalism to untested situations. Cozmin Ududec http://streamer.perimeterinstitute.ca/mp3/2bdfe5ad-006e-40aa-aaca-1a29c0b2c64e.mp3 Science http://streamer.perimeterinstitute.ca/mp3/2bdfe5ad-006e-40aa-aaca-1a29c0b2c64e.mp3 Tue, 23 Sep 2008 16:00:00 -0400 A simple theorem of Dirac identifies primary first-class constraints as generators of transformations, 'that do not affect the physical state'. This result has profound implications for the definition of physical states and observables in the quantization of constrained systems, and leads to one aspect of the infamous 'problem of time' in quantum gravity. As I will discuss, a close look at the theorem reveals that it depends crucially on the assumption of an absolute time. This assumption does not hold for reparametrization invariant theories, such as parametrized particle mechanics, and in these theories, the primary Hamiltonian constraint does generate physical change. I will also look at just what Dirac did and did not say about this case, and what has been said by reviewers since. Brendan Foster http://streamer.perimeterinstitute.ca/mp3/27de5f96-211d-4753-a8f5-21deb22746fc.mp3 Science http://streamer.perimeterinstitute.ca/mp3/27de5f96-211d-4753-a8f5-21deb22746fc.mp3 Tue, 07 Oct 2008 16:00:00 -0400 We start by studying the non-computational geometry of fractionally-dimensioned measure-zero dynamically-invariant subsets of phase space, associated with certain deterministic nonlinear dissipative dynamical systems. Then, by studying the asymptotic states of the Hawking Box, the existence of such invariant subsets is conjectured for gravitationally-bound systems. The argument hinges around the phase-space properties of black holes. Like Penrose, it is assumed that phase-space volumes shrink when the contents of the Hawking Box contain black holes. However, unlike Penrose, we do not argue for any corresponding phase-space divergence when the Box does not contain black holes. We now make the hypothesis that these invariant phase-space subsets play a primitive role in fundamental physics; specifically that the state of the universe (“reality”) lies on such an invariant subset (now and hence forever). Attention is focussed on the implications of this hypothesis for the foundations of quantum theory. For example, what are referred to as “measurements” of the quantum state, are defined in terms of symbolic dynamics on the invariant set, relative to some partition of the invariant set. This immediately leads to the notion that any theory which treats these invariant sets as primitive, must be contextual (since counterfactual perturbations almost certainly take states off the measure-zero invariant set and hence to “unreal” regions of phase space where the symbolic partition is undefined). This in turn leads to a new perspective, both on the foundations of quantum theory and on the role of gravity in formulating these foundations. In particular, a measurement-free Neo-Copenhagen Interpretation of quantum theory, based on the Invariant Set Hypothesis will be presented. Tim Palmer http://streamer.perimeterinstitute.ca/mp3/3ec5cb07-90a1-43a0-9c68-bb15084679fa.mp3 Science http://streamer.perimeterinstitute.ca/mp3/3ec5cb07-90a1-43a0-9c68-bb15084679fa.mp3 Tue, 21 Oct 2008 16:00:00 -0400 TBA Stuart Kauffman http://streamer.perimeterinstitute.ca/mp3/204d8729-6cfa-43b6-b0a5-048254e72e03.mp3 Science http://streamer.perimeterinstitute.ca/mp3/204d8729-6cfa-43b6-b0a5-048254e72e03.mp3 Tue, 28 Oct 2008 16:00:00 -0400 The unparalleled empirical success of quantum theory strongly suggests that it accurately captures fundamental aspects of the workings of the physical world. The clear articulation of these aspects is of inestimable value --- not only for the deeper understanding of quantum theory in itself, but for its further development, particularly for the development of a theory of quantum gravity. Recently, there has been growing interest in elucidating these aspects by expressing, in a less abstract mathematical language, what we think quantum theory might be telling us about how nature works, and trying to derive, or reconstruct, quantum theory from these postulates. In this talk, I describe a simple reconstruction of the finite- dimensional quantum formalism. The derivation takes places with a classical probabilistic framework equipped with the information (or Fisher-Rao) metric, and rests upon a small number of elementary ideas (such as complementarity and global gauge invariance). The complex structure of quantum formalism arises very naturally. The derivation provides a number of non-trivial insights into the quantum formalism, such as the extensive nature of the role of information geometry in determining the quantum formalism, the importance of global gauge invariance, and the importance (or lack thereof) of assumptions concerning separated systems. Philip Goyal http://streamer.perimeterinstitute.ca/mp3/1eb8c532-8496-4983-8f29-8ee270498bad.mp3 Science http://streamer.perimeterinstitute.ca/mp3/1eb8c532-8496-4983-8f29-8ee270498bad.mp3 Tue, 04 Nov 2008 16:00:00 -0500 I show that physical devices that perform observation, prediction, or recollection share an underlying mathematical structure. I call devices with that structure ``inference devices''. I present a set of existence and impossibility results concerning inference devices. These results hold independent of the precise physical laws governing our universe. In a limited sense, the impossibility results establish that Laplace was wrong to claim that even in a classical, non-chaotic universe the future can be unerringly predicted, given sufficient knowledge of the present. Alternatively, these impossibility results can be viewed as a non-quantum mechanical ``uncertainty principle''. Next I explore the close connections between the mathematics of inference devices and of Turing Machines. I end by informally discussing the philosophical implications of these results, e.g., for whether the universe ``is'' a computer. David Wolpert http://streamer.perimeterinstitute.ca/mp3/c8c2fcda-0a83-47a7-8544-3f52dc9fca5d.mp3 Science http://streamer.perimeterinstitute.ca/mp3/c8c2fcda-0a83-47a7-8544-3f52dc9fca5d.mp3 Tue, 11 Nov 2008 16:00:00 -0500 Many statistics problems involve predicting the joint strategy that will be chosen by the players in a noncooperative game. Conventional game theory predicts that the joint strategy will satisfy an ``equilibrium concept''. The relative probabilities of the joint strategies satisfying the equilibrium concept are not given, and all joint strategies that do not satisfy it are given probability zero. As an alternative, I view the prediction problem as one of statistical inference, where the ``data'' includes the details of the noncooperative game. This replaces conventional game theory's focus on how to specify a set of equilibrium joint strategies with a focus on how to specify a density function over joint strategies. I explore a Bayesian version of such a Predictive Game Theory (PGT) that provides a posterior density over joint strategies. It is based on the the entropic prior and on a likelihood that quantifies the rationalities of the players. The Quantal Response Equilibrium (QRE) is a popular game theory equilibrium concept parameterized by player rationalities. I show that for some games the local peaks of the posterior density over joint strategies approximate the associated QRE's, and derive the associated correction terms. I also discuss how to estimate parameters of the likelihood from observational data, and how to sample from the posterior. I end by showing how PGT can be used to specify a {it{unique}} equilibrium for any noncooperative game, thereby providing a solution to a long-standing problem of conventional game theory. David Wolpert http://streamer.perimeterinstitute.ca/mp3/379333f8-54d8-4351-8bb6-34c5b114d10c.mp3 Science http://streamer.perimeterinstitute.ca/mp3/379333f8-54d8-4351-8bb6-34c5b114d10c.mp3 Thu, 13 Nov 2008 16:00:00 -0500 Conventional quantum mechanics answers this question by specifying the required mathematical properties of wavefunctions and invoking the Born postulate. The ontological question remains unanswered. There is one exception to this. A variation of the Feynman chessboard model allows a classical stochastic process to assemble a wavefunction, based solely on the geometry of spacetime paths. A direct comparison of how a related process assembles a Probability Density Function reveals both how and why PDFs and wavefunctions differ from the perspective of an underlying kinetic theory. If the fine-scale motion of a particle through spacetime is continuous and position is a single valued function of time, then we are able to describe ensembles of paths directly by PDFs. However, should paths have time reversed portions so that position is not a single-valued function of time, a simple Bernoulli counting of paths fails, breaking the link to PDF's! Under certain circumstances, correcting the path-counting to accommodate time-reversed sections results in wavefunctions not PDFs. The result is that a single `switch' simultaneously turns on both special relativity and quantum propagation. Physically, fine-scale random motion in space alone yields a diffusive process with PDFs governed by the Telegraph equations. If the fine-scale motion includes both directions in time, the result is a wavefunction satisfying the Dirac equation that also provides a detailed answer to the title question. Garnet Ord http://streamer.perimeterinstitute.ca/mp3/4978c233-5a5e-49db-8270-f39dc83a3a7b.mp3 Science http://streamer.perimeterinstitute.ca/mp3/4978c233-5a5e-49db-8270-f39dc83a3a7b.mp3 Tue, 18 Nov 2008 16:00:00 -0500 Bob Batterman http://streamer.perimeterinstitute.ca/mp3/2fbc2233-2c08-4cc8-9bf0-ee697034857c.mp3 Science http://streamer.perimeterinstitute.ca/mp3/2fbc2233-2c08-4cc8-9bf0-ee697034857c.mp3 Fri, 21 Nov 2008 11:00:00 -0500 This paper critically examines the view of quantum mechanics that emerged shortly after the introduction of quantum mechanics and that has been widespread ever since. Although N. Bohr, P. A. M. Dirac, and W. Heisenberg advanced this view earlier, it is best exemplified by J. von Neumann’s argument in Mathematical Foundations of Quantum Mechanics (1932) that the transformation of 'a [quantum] state ... under the action of an energy operator . . . is purely causal,' while, 'on the other hand, the state ... which may measure a [given] quantity ... undergoes in a measurement a non-casual change.' Accordingly, while the paper discusses all four of these arguments, it will especially focus on that of von Neumann. The paper also offers an alternative, radically noncausal, view of the quantum-mechanical situation and considers the differences between the ensemble and the Bayesian understanding quantum mechanics. It will also discuss the Bayesian approach to quantum information theory in this set of contexts. Arkady Plotnitsky http://streamer.perimeterinstitute.ca/mp3/b6b3515b-ccbe-484a-876d-29703872e0dd.mp3 Science http://streamer.perimeterinstitute.ca/mp3/b6b3515b-ccbe-484a-876d-29703872e0dd.mp3 Tue, 25 Nov 2008 16:00:00 -0500 We all know that the EPR argument fails, and we can all provide proofs of one sort or another that it can't work. But in spite of this, there's something curiously tempting about the reasoning, and the temptation sometimes leads to needless perplexity about other issues. This paper will do two things. It will offer a diagnosis of where the EPR argument goes wrong that shows why we should be suspicious long before we get to Bell-type results, and then use the thought behind this diagnosis to suggest an orientation toward thinking about quantum states. The proposal for understanding states will have some things in common with Bayesian approaches, but will part company with them on some crucial points. Allen Stairs http://streamer.perimeterinstitute.ca/mp3/93c868e7-51f9-4e39-a841-30a39d36e554.mp3 Science http://streamer.perimeterinstitute.ca/mp3/93c868e7-51f9-4e39-a841-30a39d36e554.mp3 Tue, 02 Dec 2008 16:00:00 -0500 Quantum entanglement has two remarkable properties. First, according to Bell's theorem, the statistical correlations between entangled quantum systems are inconsistent with any theory of local hidden variables. Second, entanglement is monogamous -- that is, to the degree that A and B are entangled with each other, they cannot be entangled with any other systems. It turns out that these properties are intimately related. Ben Schumacher http://streamer.perimeterinstitute.ca/mp3/2a53cc39-30cb-4e06-aec3-cd9ec718afad.mp3 Science http://streamer.perimeterinstitute.ca/mp3/2a53cc39-30cb-4e06-aec3-cd9ec718afad.mp3 Wed, 03 Dec 2008 11:00:00 -0500 Lee Smolin has argued that one of the barriers to understanding time in a quantum world is our tendency to spatialize time. The question is whether there is anything in physics that could lead us to mathematically characterize time so that it is not just another funny spatial dimension. I will explore the possibility(already considered by Smolin and others) that time may be distinguished from space by what I will call a measure of Booleanity. The Bell-Kochen-Specker Theorem shows that the statistics of quantum systems (unlike that of classical systems) do not in general permit of a Boolean substructure. I will outline reasons for thinking that time is the dimension in which the Booleanity of spacetime (considered as a quantum system) varies, while space is characterized by constant Booleanity. I will not be able to give a mathematically complete characterization of the Booleanity of a region of spacetime, since that would require nothing less than knowing how to quantize spacetime; however, I will argue that something like this is needed if one is to make any sense of an ontological distinction between past, present, and future in terms of modern physics. I will also briefly consider possible objections to this view arising from the relativity of simultaneity, which (on its usual interpretation) apparently places all events on an equal ontological footing. In order to get around this we need a generalized conception of simultaneity that treats Einstein&#39;s notion of simultaneity as a special case, and which allows for equivalence classes of spacelike separate events distinguished by covariant quantities such as action, phase, and (as I will argue) any reasonable measure of Booleanity. Kent Peacock http://streamer.perimeterinstitute.ca/mp3/f1dd9e8f-7f22-4b04-a0ee-85874452cfd8.mp3 Science http://streamer.perimeterinstitute.ca/mp3/f1dd9e8f-7f22-4b04-a0ee-85874452cfd8.mp3 Tue, 16 Dec 2008 16:00:00 -0500 Both classical probability theory and quantum theory lend themselves to a Bayesian interpretation where probabilities represent degrees of belief, and where the various rules for combining and updating probabilities are but algorithms for plausible reasoning in the face of uncertainty. I elucidate the differences and commonalities of these two theories, and argue that they are in fact the only two algorithms to satisfy certain basic consistency requirements. In order to arrive at this result I develop an over-arching framework for plausible reasoning that incorporates both classical probability and quantum theory as special cases. Jochen Rau http://streamer.perimeterinstitute.ca/mp3/ed12bf7a-6326-460e-b889-68e1885d73bf.mp3 Science http://streamer.perimeterinstitute.ca/mp3/ed12bf7a-6326-460e-b889-68e1885d73bf.mp3 Tue, 13 Jan 2009 16:00:00 -0500 The essential ingredients of a quantum theory are usually a Hilbert space of states and an algebra of operators encoding observables. The mathematical operations available with these structures translate fairly well into physical operations (preparation, measurement etc.) in a non-relativistic world. This correspondence weakens in quantum field theory, where the direct operational meaning of the observable algebra structure (encoded usually through commutators) is lost. The situation becomes even worse when we want to give a more dynamical role to spacetime as for example in attempts to formulate a quantum theory of gravity. I argue that a revision of the structures that we think of as fundamental in a quantum theory is in order. I go on to outline a proposal in this direction, based on the so called 'general boundary formulation', emphasizing the operational meaning of the ingredients. If time permits I will also comment on the relation to the framework of algebraic quantum field theory. Robert Oeckl http://streamer.perimeterinstitute.ca/mp3/08a2b536-c731-404e-ba69-4965a6a8472c.mp3 Science http://streamer.perimeterinstitute.ca/mp3/08a2b536-c731-404e-ba69-4965a6a8472c.mp3 Tue, 20 Jan 2009 16:00:00 -0500 A standard canonical quantization of general relativity yields a time-independent Schroedinger equation whose solutions are static wavefunctions on configuration space. Naively this is in contradiction with the real world where things do change. Broadly speaking, the problem how to reconcile a theory which contains no concept of time with a changing world is called 'the problem of time'. In this seminar we shall study this problem using a reformulation of Newtonian mechanics due to Jacobi (Jacobi's timeless mechanics) which allows one to study the problem of time without all the technical difficulties present in quantized general relativity. We show explicitly that Jacobi's timeless mechanics is a straightforward counterexample to the claim that all first class constraints generate gauge transformations, i.e. physically indistinguishable states. The implications of this is unclear. By making use of deBroglie-Bohm trajectories we derive a necessary and sufficient condition for a time-dependent Schroedinger equation to emerge for subsystems. The importance of 'strong' entanglement between subsystem and environment for the emergence of time is stressed. Hans Westman http://streamer.perimeterinstitute.ca/mp3/f90536de-8e7c-43d7-9ee7-14e376f3af64.mp3 Science http://streamer.perimeterinstitute.ca/mp3/f90536de-8e7c-43d7-9ee7-14e376f3af64.mp3 Tue, 10 Feb 2009 16:00:00 -0500 Quantum mechanics is a non-classical probability theory, but hardly the most general one imaginable: any compact convex set can serve as the state space for an abstract probabilistic model (classical models corresponding to simplices). From this altitude, one sees that many phenomena commonly regarded as ``characteristically quantum' are in fact generically ``non-classical'. In this talk, I'll show that almost any non-classical probabilistic theory shares with quantum mechanics a notion of entanglement and, with this, a version of the so-called measurement problem. I'll then discuss what's required for an abstract probabilistic theory to admit a somewhat simplified version of Everett's response to this problem -- an exercise that turns out to be instructive in several ways. Alexander Wilce http://streamer.perimeterinstitute.ca/mp3/7c20074f-389d-4bbe-9897-719af5a4ea37.mp3 Science http://streamer.perimeterinstitute.ca/mp3/7c20074f-389d-4bbe-9897-719af5a4ea37.mp3 Tue, 03 Mar 2009 16:00:00 -0500 Quantum foundations in the light of gauge theories We will present the conjecture according to which the fact that q and p cannot be both ``observables'' of the same quantum system indicates that there is a remnant universal symmetry acting on classical states. In order to unpack this claim we will generalize to unconstrained systems the gauge correspondence between properties defined by first-class constraints and gauge symmetries generated by these constraints. As we shall see, this means that the uncertainty principle might be encoded in the very definition of the canonical variables q and p. According to the ontology of quantum objects that stems from this analysis, the quantum-mechanical description of physical objects is complete. Gabriel Catren http://streamer.perimeterinstitute.ca/mp3/c394019a-f8f0-46b8-9834-3ffef26baed8.mp3 Science http://streamer.perimeterinstitute.ca/mp3/c394019a-f8f0-46b8-9834-3ffef26baed8.mp3 Tue, 10 Mar 2009 16:00:00 -0400 Eugene Wigner and Hermann Weyl led the way in applying the theory of group representations to the newly formulated theory of quantum mechanics starting in 1927. My talk will focus, first, on two aspects of this early work. Physicists had long exploited symmetries as a way of simplifying problems within classical physics. Wigner recognized that the theory of group representations would similarly have enormous payoff in quantum mechanics, allowing him to solve problems in atomic spectroscopy ``almost without calculation.'' Here I will describe the novel aspects of symmetry in QM that Wigner clarified in the series of papers leading up to his 1931 textbook (Wigner's theorem, projective representations, etc.). The second aspect is less well-known: Weyl (1927) argued that group theory could also be used to address foundational questions in quantum mechanics, leading to a reformulation of the classical commutation relations and a proposal for quantization. Weyl's program had much less immediate impact, although it led to the Stone-von Neumann theorem and to Mackey's imprimitivity theorem. As a final historical point, I argue that in this early work the theory of group representations was optional (as emphasized by Slater and others) in a sense that it was not in particle physics in the 60s. The closing section of the talk turns to philosophical morals that have been drawn from this historical episode, in particular claims regarding ontic structural realism (French, Ladyman) and the group-theoretic constitution of objects (Castellani). Chris Smeenk http://streamer.perimeterinstitute.ca/mp3/cdeb5c9d-8a8a-478f-87b5-98258646dbb2.mp3 Science http://streamer.perimeterinstitute.ca/mp3/cdeb5c9d-8a8a-478f-87b5-98258646dbb2.mp3 Thu, 12 Mar 2009 16:00:00 -0400 We know the mathematical laws of quantum mechanics, but as yet we are not so sure why those laws should be inevitable. In the simpler but related environment of classical inference, we also know the laws (of probability). With better understanding of quantum mechanics as the eventual goal, Kevin Knuth and I have been probing the foundations of inference. The world we wish to infer is a partially-ordered set ('poset') of states, which may as often supposed be exclusive, but need not be (e.g. A might be a requirement for B). In inference, a state of mind about the world degrades from perfect knowledge through logical OR, which allows for uncertain alternatives. We don't need AND, and we don't need NOT; we just need OR. This display of acceptable states of mind is [close to] a mathematical 'lattice'. We find that the OR structure by itself (!) forces the ordinary rules of probability calculus. No other rules are compatible with the structure of a lattice, so the ordinary rules are inevitable. The standard Shannon information/entropy is likewise inevitable. Taking this idea further, the OR of states of mind gives a lattice of 'Questions' that might be useful for automated learning. Disconcertingly, this lattice is very much larger (in class aleph-2), and the natural valuations on it exhibit large range. I will present this extension, and ask whether we can rationally foresee its use in practical application. John Skilling http://streamer.perimeterinstitute.ca/mp3/25af08ac-4fbd-452c-a9eb-6ca27f8f1e41.mp3 Science http://streamer.perimeterinstitute.ca/mp3/25af08ac-4fbd-452c-a9eb-6ca27f8f1e41.mp3 Tue, 31 Mar 2009 16:00:00 -0400 Researchers in quantum foundations claim (D'Ariano, Fuchs, ...): Quantum = probability theory + x and hence: x = Quantum - probability theory Guided by the metaphorical analogy: probability theory / x = flesh / bones we introduce a notion of quantum measurement within x, which, when flesing it with Hilbert spaces, provides orthodox quantum mechanical probability calculus. Bob Coecke http://streamer.perimeterinstitute.ca/mp3/5d408b52-3089-48a6-9a87-8c3b93f67e5e.mp3 Science http://streamer.perimeterinstitute.ca/mp3/5d408b52-3089-48a6-9a87-8c3b93f67e5e.mp3 Tue, 05 May 2009 16:00:00 -0400 Although most realistic approaches to quantum theory are based on classical particles, QFT reveals that classical fields are a much closer analog. And unlike quantum fields, classical fields can be extrapolated to curved spacetime without conceptual difficulty. These facts make it tempting to reconsider whether quantum theory might be reformulated on an underlying classical field structure. This seminar aims to demonstrate that by changing only how boundary conditions (BCs) are imposed on ordinary classical field equations, a psi-epistemic quantum theory naturally emerges. Uncertainty and basic quantization naturally result from imposing BCs on closed hypersurfaces (as in Lagrangian QFT); further quantization results from extending Hamilton's principle to restrict the BCs as well as the field equations. The partial dependence of field parameters on future BCs implies an effective contextuality, naturally avoiding the usual arguments against realistic quantum models. Successful applications to the relativistic scalar field will be presented, further motivating an ambitious research program of reformulating quantum theory in terms of ontic classical fields. Kenneth Wharton http://streamer.perimeterinstitute.ca/mp3/f5af583b-eb5a-4213-bf76-def71d38e65d.mp3 Science http://streamer.perimeterinstitute.ca/mp3/f5af583b-eb5a-4213-bf76-def71d38e65d.mp3 Tue, 16 Jun 2009 16:00:00 -0400 Violation of local realism can be probed by theory&ndash;independent tests, such as Bell&rsquo;s inequality experiments. There, a common assumption is the existence of perfect, classical, reference frames, which allow for the specification of measurement settings with arbitrary precision. However, if the reference frames are ``bounded'', only limited precision can be attained. We expect then that the finiteness of the reference frames limits the observability of genuine quantum features. Using spin coherent states as reference frames, we determined their minimal size necessary to violate Bell&rsquo;s inequalities in entangled systems ranging from qubits to macroscopic dimensions. In the latter, the reference frame&rsquo;s size must be quadratically larger than that of the system. Lacking such large reference frames, precludes quantum phenomena from appearing in everyday experience. Fabio Costa http://streamer.perimeterinstitute.ca/mp3/2ed969cf-7e58-4fa7-b478-0fe08f100db1.mp3 Science http://streamer.perimeterinstitute.ca/mp3/2ed969cf-7e58-4fa7-b478-0fe08f100db1.mp3 Tue, 04 Aug 2009 16:00:00 -0400 Betting (or gambling) is a useful tool for studying decision-making in the face of [classical] uncertainty. We would like to understand how a quantum &quot;agent&quot; would act when faced with uncertainty about its [quantum] environment. I will present a preliminary construction of a theory of quantum gambling, motivated by roulette and quantum optics. I'll begin by reviewing classical gambling and the Kelly Criterion for optimal betting. Then I'll demonstrate a quantum optical version of roulette, and discuss some of the challenges and pitfalls in designing such analogues. Quantum agents have access to many more strategies than classical agents. Quantum strategies provide no advantage in classical roulette, but I'll show that a quantum agent can outperform a classical agent in quantum roulette. Grant Salton http://streamer.perimeterinstitute.ca/mp3/59a00a73-1940-4ced-84a8-dac2e11d6424.mp3 Science http://streamer.perimeterinstitute.ca/mp3/59a00a73-1940-4ced-84a8-dac2e11d6424.mp3 Tue, 08 Sep 2009 16:00:00 -0400 We present a first-principles implementation of {em spatial} scale invariance as a local gauge symmetry in geometry dynamics using the method of best matching. In addition to the 3-metric, the proposed scale invariant theory also contains a 3-vector potential A_k as a dynamical variable. Although some of the mathematics is similar to Weyl's ingenious, but physically questionable, theory, the equations of motion of this new theory are second order in time-derivatives. It is tempting to try to interpret the vector potential A_k as the electromagnetic field. We exhibit four independent reasons for not giving into this temptation. A more likely possibility is that it can play the role of ``dark matter''. Indeed, as noted in scale invariance seems to play a role in the MOND phenomenology. Spatial boundary conditions are derived from the free-endpoint variation method and a preliminary analysis of the constraints and their propagation in the Hamiltonian formulation is presented. Hans Westman http://streamer.perimeterinstitute.ca/mp3/e20c890c-b0e2-4946-be9f-f2ab1ac17c57.mp3 Science http://streamer.perimeterinstitute.ca/mp3/e20c890c-b0e2-4946-be9f-f2ab1ac17c57.mp3 Tue, 15 Sep 2009 16:00:00 -0400 I will present recent work [1] on preparation by measurement of Greenberger&ndash;Horne&ndash;Zeilinger (GHZ) states in circuit quantum electrodynamics. In particular, for the 3-qubit case, when employing a nonlinear filter on the recorded homodyne signal the selected states are found to exhibit values of the Bell&ndash;Mermin operator exceeding 2 under realistic conditions. I will discuss the potential of the dispersive readout to demonstrate a violation of the Mermin bound, and present a measurement scheme avoiding the necessity for full detector tomography. [1] Lev S Bishop et al 2009 New J. Phys. 11 073040 Lev Bishop http://streamer.perimeterinstitute.ca/mp3/54308722-56ea-46b9-9586-0214a411fadf.mp3 Science http://streamer.perimeterinstitute.ca/mp3/54308722-56ea-46b9-9586-0214a411fadf.mp3 Tue, 22 Sep 2009 16:00:00 -0400 Instrumentalism about the quantum state is the view that this mathematical object does not serve to represent a component of (non-directly observable) reality, but is rather a device solely for making predictions about the results of experiments. One honest way to be such an instrumentalist is a) to take an ensemble view (= frequentism about quantum probabilities), whereby the state represents predictions for measurement results on ensembles of systems, but not individual systems and b) to assign some specific level for the quantum/classical cut. But what happens if one drops (b), or (a), or both, as some have been inclined to? Can one achieve a consistent view then? A major worry is illustrated by the Wigner's friend scenario: it looks as if it should make a measurable difference where one puts the cut, so how can it be consistent to slide it around (as, e.g., Bohr was wont to)? I'll discuss two main cases: that of Asher Peres' book, which adopts (a) but drops (b); and that of the quantum Bayesians Caves, Fuchs and Shack, which drops both. A view of Peres' sort can I, think, be made consistent, though may look a little strained; the quantum Bayesians' can too, though there are some subtleties (which I shall discuss) about how one should handle Wigner's friend. Christopher Timpson http://streamer.perimeterinstitute.ca/mp3/765b38ed-78ad-4afb-bb05-81516f01eecd.mp3 Science http://streamer.perimeterinstitute.ca/mp3/765b38ed-78ad-4afb-bb05-81516f01eecd.mp3 Fri, 25 Sep 2009 11:00:00 -0400 Bruno de Finetti is one of the founding fathers of the subjectivist school of probability, where probabilities are interpreted as rational degrees of belief. His work on the relation between the theorems of the probability calculus and rationality is among the corner stones of modern subjective probability theory. De Finetti maintained that rationality requires that an agent&rsquo;s degrees of belief be coherent. I argue that de Finetti held that the coherence conditions of degrees of belief in events depend on their verifiability. On this view, the familiar constraints of coherence only apply to sets of degrees of belief that could in principle be jointly verified. Accordingly, the constraints that coherence imposes on degrees of belief are generally weaker than the familiar ones. I then consider the implications of this interpretation of de Finetti for probabilities in quantum mechanics, focusing on the EPR/Bohm experiment and Bell&rsquo;s theorem. Jossi Berkovitz http://streamer.perimeterinstitute.ca/mp3/2cbcec08-7413-4c5a-b7da-656f2c8e230f.mp3 Science http://streamer.perimeterinstitute.ca/mp3/2cbcec08-7413-4c5a-b7da-656f2c8e230f.mp3 Fri, 09 Oct 2009 11:00:00 -0400 A closer look at some proposed Gedanken-experiments on BECs promises to shed light on several aspects of reduction and emergence in physics. These include the relations between classical descriptions and different quantum treatments of macroscopic systems, and the emergence of new properties and even new objects as a result of spontaneous symmetry breaking. Richard Healey http://streamer.perimeterinstitute.ca/mp3/8afc48f9-0c11-4406-8ae0-ecc8c25d4ae0.mp3 Science http://streamer.perimeterinstitute.ca/mp3/8afc48f9-0c11-4406-8ae0-ecc8c25d4ae0.mp3 Thu, 29 Oct 2009 11:30:00 -0400 In his brilliant article &quot;Against 'Measurement'&quot;, John Bell famously argued that the word has had such a damaging effect on the discussion, that it should now be banned altogether in quantum mechanics. But in the beginning was the word, and the word is still with us. Indeed, David Mermin responded In Praise of Measurement that within the field of quantum computer science the concept of measurement is precisely defined, unproblematic, and forms the foundation of the entire subject, a verdict reaffirmed by the development of measurement-based quantum computation. Bell's arguments deserve a more direct response: I shall try to give one. Richard Healey http://streamer.perimeterinstitute.ca/mp3/7969f67d-e219-4765-88cc-7056709a03c3.mp3 Science http://streamer.perimeterinstitute.ca/mp3/7969f67d-e219-4765-88cc-7056709a03c3.mp3 Tue, 17 Nov 2009 16:00:00 -0500 For a quantum system with a d-dimensional Hilbert space, a symmetric informationally complete measurement (SIC) can be thought of as a set of d^2 pure states all having the same overlap. Constructions of SICs for composite systems usually do not make use of the composite structure but treat the system as a whole. Indeed for some cases, one can prove that a SIC cannot have the symmetry that one naturally associates with the composite structure. In this talk I give one example showing how a SIC for three qubits can be constructed from SICs for the individual qubits. I ask whether the strategy used in this example might apply to other composite cases. William Wootters http://streamer.perimeterinstitute.ca/mp3/12c200b8-8728-4b07-a435-7efbfdf82dd4.mp3 Science http://streamer.perimeterinstitute.ca/mp3/12c200b8-8728-4b07-a435-7efbfdf82dd4.mp3 Tue, 01 Dec 2009 16:00:00 -0500 CMB measurements reveal a very smooth early universe. We propose a mech- anism to make this smoothness natural by weakening the strength of gravity at early times, and therefore altering which initial conditions have low entropy. Simon Judes http://streamer.perimeterinstitute.ca/mp3/e5761c0d-c9be-4786-8cd5-1e76b085d924.mp3 Science http://streamer.perimeterinstitute.ca/mp3/e5761c0d-c9be-4786-8cd5-1e76b085d924.mp3 Mon, 07 Dec 2009 12:00:00 -0500 In this talk I will report on a recent work [arXiv:0908.1583], which investigates general probabilistic theories where every mixed state has a purification, unique up to reversible channels on the purifying system. The purification principle is equivalent to the existence of a reversible realization for every physical process, namely that to the fact that every physical process can be regarded as arising from the reversible interaction of the input system with an environment that is eventually discarded. From the purification principle one can also construct an isomorphism between transformations and bipartite states that possesses all structural properties of the Choi-Jamiolkowski isomorphism in Quantum Mechanics. Such an isomorphism allows one to prove most of the basic features of Quantum Information Processing, like e.g. no information without disturbance, no joint discrimination of all pure states, no cloning, teleportation, complementarity between correctable and deletion channels, no programming, and no bit commitment, without resorting to the mathematical framework of Hilbert spaces. Giulio Chiribella http://streamer.perimeterinstitute.ca/mp3/21d5481e-a826-431a-a011-65dd90386a05.mp3 Science http://streamer.perimeterinstitute.ca/mp3/21d5481e-a826-431a-a011-65dd90386a05.mp3 Tue, 02 Feb 2010 16:00:00 -0500 How can we describe a device that takes two unknown operational boxes and conditionally on some input variable connects them in different orders? In order to answer this question, I will introduce maps from transformations to transformations within operational probabilistic theories with purification, and show their characterisation in terms of operational circuits. I will then proceed exploring the hierarchy of maps on maps. A particular family of maps in the hierarchy are the ones whose output is in the set of transformations. These maps can be fully characterised by their correspondence with channels with memory, and it is exactly the family of transformations that can be implemented through operational circuits. I will then show the problems that arise in defining the remainder of the hierarchy, and the reason why we cannot avoid considering its elements. The main consequence of admitting the generalised transformations as possible within the operational theory is that we cannot describe them in terms of simple causal connection of transformations in a circuit with a fixed causal structure. In quantum theory, we can understand such higher order transformations in terms of superpositions of circuits with different causal structures. The problem whether computations exploiting higher-order transformations can be efficiently simulated by a conventional circuital computer is posed. Paolo Perinotti http://streamer.perimeterinstitute.ca/mp3/9470f266-49ef-420d-9717-66979fb366fc.mp3 Science http://streamer.perimeterinstitute.ca/mp3/9470f266-49ef-420d-9717-66979fb366fc.mp3 Tue, 02 Feb 2010 17:00:00 -0500 In this talk, I will demonstrate that correlations inconsistent with any locally causal description can be a generic feature of measurements on entangled quantum states. Specifically, spatially-separated parties who perform local measurements on a maximally-entangled state using randomly chosen measurement bases can, with significant probability, generate nonclassical correlations that violate a Bell inequality. For n parties using a Greenberger-Horne-Zeilinger state, this probability of violation rapidly tends to unity as the number of parties increases. Moreover, even with both a randomly chosen two-qubit pure state and randomly chosen measurement bases, a violation can be found about 10% of the time. Amongst other applications, our work provides a feasible alternative for the demonstration of Bell inequality violation without a shared reference frame. Yeong-Cherng Liang http://streamer.perimeterinstitute.ca/mp3/c72e6c55-dfc7-40db-baf4-847c7f8f54b6.mp3 Science http://streamer.perimeterinstitute.ca/mp3/c72e6c55-dfc7-40db-baf4-847c7f8f54b6.mp3 Thu, 04 Feb 2010 16:00:00 -0500 In the Scholium in Newton's Principia which contains the discussions about absolute space, time, and the bucket experiment, Newton also posed a problem that Julian Barbour has denoted the &quot;Scholium problem&quot;. Newton writes there &quot;But how are we to obtain the true motions from their causes, effects, and apparent differences, and the converse, shall be explained more at large in the following treatise. For to this end it was that I composed it&quot;. This problem was clearly considered very important by Newton who claims he wrote the Principia dedicated to this problem. Interestingly Newton never returned to the problem. In this talk we are going to give a mathematical precise formulation of the Scholium problem. A subpart of the Scholium problem consists of determining how accurate the observers clock is. We are going to start from that end and see that the problem of defining duration is inseparately intertwined with the full scholium problem. Hans Westman http://streamer.perimeterinstitute.ca/mp3/6fdc3578-9f3d-474f-9054-87559284440c.mp3 Science http://streamer.perimeterinstitute.ca/mp3/6fdc3578-9f3d-474f-9054-87559284440c.mp3 Tue, 09 Mar 2010 16:00:00 -0500 The Wheeler delayed choice experiment, Elitzur-Vaidman interaction-free measurement, and Hosten-Kwiat counterfactual computation will be discussed to answer Bohr's forbidden question: &quot;Where is a quantum particle while it is inside a Mach-Zehnder Interferometer?&quot;. I will argue that the naive application of Wheeler's approach fails to explain a weak trace left by the particle and that the two-state vector description is required. Lev Vaidman http://streamer.perimeterinstitute.ca/mp3/4113bab6-f346-4637-8b5e-894e115a0a6e.mp3 Science http://streamer.perimeterinstitute.ca/mp3/4113bab6-f346-4637-8b5e-894e115a0a6e.mp3 Tue, 16 Mar 2010 16:30:00 -0400 Our starting point is a particular `canvas' aimed to `draw' theories of physics, which has symmetric monoidal categories as its mathematical backbone. With very little structural effort (i.e. in very abstract terms) and in a very short time this categorical quantum mechanics research program has reproduced a surprisingly large fragment of quantum theory. Philosophically speaking, this framework shifts the conceptual focus from `material carriers' such as particles, fields, or other `material stuff', to `logical flows of information', by mainly encoding how things stand in relation to each other. These relations could, for example, be induced by operations. Composition of these relations is the carrier of all structure. Thus far the causal structure has been treated somewhat informally within this approach. In joint work with my student Raymond Lal, by restricting the capabilities to compose, we were able to formally encode causal connections. We call the resulting mathematical structure a CauCat, since it combines the symmetric monoidal stricture with Sorkin's CauSets within a single mathematical concept. The relations which now respect causal structure are referred to as processes, which make up the actual `happenings'. As a proof of concept, we show that if in a quantum teleportation protocol one omits classical communication, no information is transfered. We also characterize Galilean theories. Classicality is an attribute of certain processes, and measurements are special kinds of processes, defined in terms of their capabilities to correlate other processes to these classical attributes. So rather than quantization, what we do is classicization within our universe of processes. We show how classicality and the causal structure are tightly intertwined. All of this is still very much work in progress! Bob Coecke http://streamer.perimeterinstitute.ca/mp3/c2e54b98-f81d-479f-b3a1-e8bfa6d50ce2.mp3 Science http://streamer.perimeterinstitute.ca/mp3/c2e54b98-f81d-479f-b3a1-e8bfa6d50ce2.mp3 Tue, 30 Mar 2010 16:00:00 -0400 One might have hoped that philosophers had sorted out what &lsquo;truth&rsquo; is supposed to be by now. After all, Aristotle offered what seems to be a clear and simple characterization in his Metaphysics. So perhaps it is surprising (and then again perhaps it isn&rsquo;t), that contemporary philosophers have not settled on a consensus regarding the nature of truth to this day. In fact, the most obvious theory of truth, that truth consists in correspondence to the facts, seems to be steadily waning in popularity in technical circles, replaced instead by a perhaps puzzlingly austere minimalist theory that restricts its characterization of truth to the familiar equivalence schema: &lt;p&gt; is true if and only if p. The differences between such deflationary theories and the &lsquo;traditional&rsquo; correspondence theory of truth, and perhaps even more strikingly between these theories and epistemic theories of truth, call to mind counterpart features in different attitudes about the proper interpretation of quantum mechanics. By reviewing the most striking features of different theories of truth, as well as some of their most difficult objections, we can start to see where different interpretations seem to be reliant on (or at least quite congenial to) particular theories of truth and also where these theories begin to reveal themselves as variously helping and hindering the smooth functioning of different interpretations. Nora Boyd http://streamer.perimeterinstitute.ca/mp3/99fb19ce-2c68-4cf2-b4e7-e872f168dd7a.mp3 Science http://streamer.perimeterinstitute.ca/mp3/99fb19ce-2c68-4cf2-b4e7-e872f168dd7a.mp3 Mon, 12 Apr 2010 11:00:00 -0400 Many putative explanations in physics rely on idealized models of physical systems. These explanations are inconsistent with standard philosophical accounts of explanation. A common view holds that idealizations can underwrite explanation nonetheless, but only when they are what have variously been called Galilean, approximative, traditional or controllable. Controllability is the least vague of these categories, and this paper focuses on the relation between controllability and explanation. Specifically, it argues that the common view is an untenable half-measure. It gives the example of a simple pendulum with quadratic damping, an uncontrollable idealization that makes use of singular limits and for which the behaviour at the limit is qualitatively new&mdash;but a system whose behaviour is fully explained in terms of the idealization. It shows that uncontrollable idealizations can have explanatory capacities (and in a way distinct from Batterman&rsquo;s &ldquo;asymptotic explanation&rdquo;). Andrew Wayne http://streamer.perimeterinstitute.ca/mp3/01500db4-c71c-4a00-a244-336986d88dfd.mp3 Science http://streamer.perimeterinstitute.ca/mp3/01500db4-c71c-4a00-a244-336986d88dfd.mp3 Fri, 23 Apr 2010 11:00:00 -0400 Non-relativistic quantum mechanics is derived as an example of entropic inference. The basic assumption is that the position of a particle is subject to an irreducible uncertainty of unspecified origin. The corresponding probability distributions constitute a curved statistical manifold. The probability for infinitesimally small changes is obtained from the method of maximum entropy and the concept of time is introduced as a book-keeping device to keep track of how they accumulate. This requires introducing appropriate notions of instant and of duration. A welcome feature is that this entropic notion of time incorporates a natural distinction between past and future. The Schroedinger equation is recovered when the statistical manifold participates in the dynamics in such a way that there is a conserved energy: its curved geometry guides the motion of the particles while they, in their turn, react back and determine its evolving geometry. The phase of the wave function&mdash;not just its magnitude&mdash;is explained as a feature of purely statistical origin. Finally, the model is extended to include external electromagnetic fields and gauge transformations. Ariel Caticha http://streamer.perimeterinstitute.ca/mp3/c24894e8-5711-4b62-b58d-a38745b2fcfb.mp3 Science http://streamer.perimeterinstitute.ca/mp3/c24894e8-5711-4b62-b58d-a38745b2fcfb.mp3 Tue, 04 May 2010 16:00:00 -0400 We first discuss quantum measure and integration theory. We then consider various anhomomorphic logics. Finally, we present some connections between the two theories. One connection is transferring a quantum measure to a measure on an anhomomorphic logic. Another is the creation of a reality filter that is stronger than Sorkin's preclusivity. This is accomplished by generating a preclusive coevent from a quantum measure. No prior knowledge of quantum measure theory or anhomomorphic logics will be assumed. Stanley Gudder http://streamer.perimeterinstitute.ca/mp3/1a40afed-ac7d-4153-b25b-b67ac5b3c7b1.mp3 Science http://streamer.perimeterinstitute.ca/mp3/1a40afed-ac7d-4153-b25b-b67ac5b3c7b1.mp3 Tue, 11 May 2010 16:00:00 -0400 It has long been recognized that there are two distinct laws that go by the name of the Second Law of Thermodynamics. The original says that there can be no process resulting in a net decrease in the total entropy of all bodies involved. A consequence of the kinetic theory of heat is that this law will not be strictly true; statistical fluctuations will result in small spontaneous transfers of heat from a cooler to a warmer body. The currently accepted version of the Second Law is probabilistic: tiny spontaneous transfers of heat from a cooler to a warmer body will be occurring all the time, while a larger transfer is not impossible, merely improbable. There can be no process whose expected result is a net decrease in total entropy. According to Maxwell, the Second Law has only statistical validity, and this statement is easily read as an endorsement of the probabilistic version. I argue that a close reading of Maxwell, with attention to his use of &quot;statistical,&quot; shows that the version of the second law endorsed by Maxwell is strictly weaker than our probabilistic version. According to Maxwell, even the probable truth of the second law is limited to situations in which we deal with matter only in bulk and are unable to observe or manipulate individual molecules. Maxwell's version does not rule out a device that could, predictably and reliably, transfer heat from a cooler to a warmer body without a compensating increase in entropy. I will discuss the evidence we have for these two laws, Maxwell's and ours. Wayne Myrvold http://streamer.perimeterinstitute.ca/mp3/88933fd2-ef5f-44b8-b9df-e993cea5a364.mp3 Science http://streamer.perimeterinstitute.ca/mp3/88933fd2-ef5f-44b8-b9df-e993cea5a364.mp3 Fri, 11 Jun 2010 11:00:00 -0400 Many results have been recently obtained regarding the power of hypothetical closed time-like curves (CTC&rsquo;s) in quantum computation. Most of them have been derived using Deutsch&rsquo;s influential model for quantum CTCs [D. Deutsch, Phys. Rev. D 44, 3197 (1991)]. Deutsch&rsquo;s model demands self-consistency for the time-travelling system, but in the absence of (hypothetical) physical CTCs, it cannot be tested experimentally. In this paper we show how the one-way model of measurement-based quantum computation (MBQC) can be used to test Deutsch&rsquo;s model for CTCs. Using the stabilizer formalism, we identify predictions that MBQC makes about a specific class of CTCs involving travel in time of quantum systems. Using a simple example we show that Deutsch&rsquo;s formalism leads to predictions conflicting with those of the one-way model. There exists an alternative, little-discussed model for quantum time-travel due to Bennett and Schumacher (in unpublished work, see http://bit.ly/cjWUT2), which was rediscovered recently by Svetlichny [arXiv:0902.4898v1]. This model uses quantum teleportation to simulate (probabilistically) what would happen if one sends quantum states back in time. We show how the Bennett/ Schumacher/ Svetlichny (BSS) model for CTCs fits in naturally within the formalism of MBQC. We identify a class of CTC&rsquo;s in this model that can be simulated deterministically using techniques associated with the stabilizer formalism. We also identify the fundamental limitation of Deutsch's model that accounts for its conflict with the predictions of MBQC and the BSS model. This work was done in collaboration with Raphael Dias da Silva and Elham Kashefi, and has appeared in preprint format (see website). Website: http://arxiv.org/abs/1003.4971 Ernesto Galvao http://streamer.perimeterinstitute.ca/mp3/02057770-f6ea-4c01-bdd1-1a9e9329fa9b.mp3 Science http://streamer.perimeterinstitute.ca/mp3/02057770-f6ea-4c01-bdd1-1a9e9329fa9b.mp3 Fri, 16 Jul 2010 14:00:00 -0400 Quantum states are not observables like in any wave mechanics but co-observables describing the reality as a possible knowledge about the statistics of all quantum events, like quantum jumps, quantum decays, quantum diffusions, quantum trajectories, etc. However, as we show, the probabilistic interpretation of the traditional quantum mechanics is inconsistent with the probbilistic causality and leads to the infamous quantum measurement problem. Moreover, we prove that all attempts to solve this problem as suggested by Bohr are doomed in the traditional framework of the reversible interactions. We explore the only possibility left to resolve the quantum causality problem while keeping the reversibility of Schroedinger mechanics. This is to break the time symmetry of the Heisenberg mechanics using the nonequivalence of the Schroedinger and Heisenberg quantum mechanics on nonsimple operator algebras in infinite dimensional Hilbert spaces. This is the main idea of Eventum Mechanics, which enhances the quantum world of the future by classical events of the past and constructs the reversible Schroedinger evolutions compatible with observable quantm trajectories by irreversible quantum to classicl interfaces in terms of the reversible unitary scatterings. It puts the idea of hidden variables upside down by declaring that what is visible (in the past by now) is not quantum but classical and what is visible (by now in the future) is quantum but not classical. More on the philosophy of Eventum Mechanics can be found in [1]. We demonstrate these ideas on the toy model of the nontrivial quantum - classical bit interface. The application of these ideas in the continuous time leads to derivation of the quantum stochastic master equations reviewed in [1] and of my research pages [3]. V. P. Belavkin: Quantum Causality, Stochastics, Trajectories and Information. Reports on Progress in Physics 65 (3): 353-420 (2002). quant-ph/0208087, PDF. http://www.maths.nott.ac.uk/personal/vpb/vpb_research.html http://www.maths.nott.ac.uk/personal/vpb/research/cau_idy.html Viacheslav Belavkin http://streamer.perimeterinstitute.ca/mp3/9ac24355-ea89-4479-b5c5-3c66d3a63a3b.mp3 Science http://streamer.perimeterinstitute.ca/mp3/9ac24355-ea89-4479-b5c5-3c66d3a63a3b.mp3 Tue, 31 Aug 2010 16:00:00 -0400 A brief review of some recent work on the causal set approach to quantum gravity. Causal sets are a discretisation of spacetime that allow the symmetries of GR to be preserved in the continuum approximation. One proposed application of causal sets is to use them as the histories in a quantum sum-over-histories, i.e. to construct a quantum theory of spacetime. It is expected by many that quantum gravity will introduce some kind of fuzziness uncertainty and perhaps discreteness into spacetime, and generic effects of this fuzziness are currently being sought. Applied as a model of discrete spacetime, causal sets can be used to construct simple phenomenological models which allow us to understand some of the consequences of this general expectation. Joe Henson http://streamer.perimeterinstitute.ca/mp3/2a456261-d1af-42a9-b71f-322cec16f998.mp3 Science http://streamer.perimeterinstitute.ca/mp3/2a456261-d1af-42a9-b71f-322cec16f998.mp3 Tue, 14 Sep 2010 16:00:00 -0400 The uncertainty principle bounds the uncertainties about the outcomes of two incompatible measurements, such as position and momentum, on a particle. It implies that one cannot predict the outcomes for both possible choices of measurement to arbitrary precision, even if information about the preparation of the particle is available in a classical memory. However, if the particle is prepared entangled with a quantum memory, it is possible to predict the outcomes for both measurement choices precisely. I will explain a recent extension of the uncertainty principle to incorporate this case. The new relation gives a lower bound on the uncertainties, which depends on the amount of entanglement between the particle and the quantum memory. If time permits, I will also outline a couple of applications. Roger Colbeck http://streamer.perimeterinstitute.ca/mp3/98e4ce8a-db42-40ac-97b6-4dc1bf5fe9c1.mp3 Science http://streamer.perimeterinstitute.ca/mp3/98e4ce8a-db42-40ac-97b6-4dc1bf5fe9c1.mp3 Tue, 28 Sep 2010 16:00:00 -0400 The question of the existence of gravitational stress-energy in general relativity has exercised investigators in the field since the very inception of the theory. Folklore has it that no adequate definition of a localized gravitational stress-energetic quantity can be given. Most arguments to that effect invoke one version or another of the Principle of Equivalence. I argue that not only are such arguments of necessity vague and hand-waving but, worse, are beside the point and do not address the heart of the issue. Based on an analysis of what it may mean for one tensor to depend in the proper way on another, I prove that, under certain natural conditions, there can be no tensor whose interpretation could be that it represents gravitational stress-energy in general relativity. It follows that gravitational energy, such as it is in general relativity, is necessarily non-local. Along the way, I prove a result of some interest in own right about the structure of the associated jet bundles of the bundle of Lorentz metrics over spacetime. Erik Curiel http://streamer.perimeterinstitute.ca/mp3/4eac67df-4d52-462e-8bcf-381bfa2879c6.mp3 Science http://streamer.perimeterinstitute.ca/mp3/4eac67df-4d52-462e-8bcf-381bfa2879c6.mp3 Fri, 01 Oct 2010 11:00:00 -0400 In this talk we quickly review the basics of the modal &quot;toy model&quot; of quantum theory described by Schumacher in his September 22 colloquium at PI. We then consider how the theory addresses more general open systems. Because the modal theory has a more primitive mathematical structure than actual quantum mechanics, it lacks density operators, positive operator measurements, and completely positive maps. As we will show, however, modal quantum theory has an elegant description of the states, effects and operations of open modal systems -- a description with close analogies to actual quantum mechanics. Mike Westmoreland http://streamer.perimeterinstitute.ca/mp3/2bb5f912-fbba-4156-aed6-4d05af250cc9.mp3 Science http://streamer.perimeterinstitute.ca/mp3/2bb5f912-fbba-4156-aed6-4d05af250cc9.mp3 Tue, 05 Oct 2010 16:00:00 -0400 I revisit an example of stronger-than-quantum correlations that was discovered by Ernst Specker in 1960. The example was introduced as a parable wherein an over-protective seer sets a simple prediction task to his daughter's suitors. The challenge cannot be met because the seer asks the suitors for a noncontextual assignment of values but measures a system for which the statistics are inconsistent with such an assignment. I will show how by generalizing these sorts of correlations, one is led naturally to some well-known proofs of nonlocality and contextuality, and to some new ones. Specker's parable involves a kind of complementarity that does not arise in quantum theory - three measurements that can be implemented jointly pairwise but not triplewise -- and therefore prompts the question of what sorts of foundational principles might rule out this kind of complementarity. This is joint work with Howard Wiseman and Yeong-Cherng Liang. Robert Spekkens http://streamer.perimeterinstitute.ca/mp3/e4747919-02e9-4f81-9eab-88102e4f6811.mp3 Science http://streamer.perimeterinstitute.ca/mp3/e4747919-02e9-4f81-9eab-88102e4f6811.mp3 Tue, 12 Oct 2010 16:00:00 -0400 Landauer's erasure principle states that there is an inherent work cost associated with all irreversible operations, like the erasure of the data stored in a system. The necessary work is determined by our uncertainty: the more we know about the system, the less it costs to erase it. Here, we analyse erasure in a general setting where our information about that system can be quantum mechanical. In this scenario, our uncertainty, measured by a conditional entropy, may become negative. We establish a general relation between quantum conditional entropies and a physical quantity, the work cost of erasure. As a consequence, we obtain a thermodynamic interpretation of negative entropies: they quantify the work that can be gained by a quantum observer erasing a system. (arXiv: 1009.1630) Lidia del Rio http://streamer.perimeterinstitute.ca/mp3/0848e391-b803-4e80-94ae-84f8cb88bc5b.mp3 Science http://streamer.perimeterinstitute.ca/mp3/0848e391-b803-4e80-94ae-84f8cb88bc5b.mp3 Tue, 19 Oct 2010 16:00:00 -0400 Nonlocality is the most striking feature of quantum mechanics. It might even be considered its defining feature and understanding it may be the most important step towards understanding the whole theory. Yet for a long time it was impossible to pinpoint the reason behind the exact amount of nonlocality allowed by quantum mechanics expressed by Tsirelson bound. Recently information causality has been shown to be the principle from which this bound can be derived. However the whole set of nonlocal correlations and nonlocal information processing protocols that quantum mechanics allows is not specified by the Tsirelson bound. It remains an open question whether this whole zoo of nonlocality can be derived from information causality. In this talk I present the fields where information causality is applied together with most recent results or lack of such. Marcin Pawlowski http://streamer.perimeterinstitute.ca/mp3/0dd8ef22-32ce-46cb-b95a-c8005a73b3a6.mp3 Science http://streamer.perimeterinstitute.ca/mp3/0dd8ef22-32ce-46cb-b95a-c8005a73b3a6.mp3 Tue, 16 Nov 2010 16:00:00 -0500 TBA Margaret Morrison http://streamer.perimeterinstitute.ca/mp3/de7e8850-2b11-4604-801d-a72c98672f30.mp3 Science http://streamer.perimeterinstitute.ca/mp3/de7e8850-2b11-4604-801d-a72c98672f30.mp3 Fri, 19 Nov 2010 11:00:00 -0500 The second law of thermodynamics tells that physics imposes a fundamental constraint on the efficiency of all thermal machines. Here I will address the question of whether size imposes further constraints upon thermal machines, namely whether there is a minimum size below which no machine can run, and whether when they are small if they can still be efficient? I will present a simple model which shows that there is no size limitation and no limit on the efficiency of thermal machine and that this leads to a unified view of small refrigerators, pumps and engines. Paul Skrzypczyk http://streamer.perimeterinstitute.ca/mp3/0ecdf661-f6f7-4e95-bcba-6de1398b81bd.mp3 Science http://streamer.perimeterinstitute.ca/mp3/0ecdf661-f6f7-4e95-bcba-6de1398b81bd.mp3 Tue, 23 Nov 2010 16:00:00 -0500 I will review some recent advances on the line of deriving quantum field theory from pure quantum information processing. The general idea is that there is only Quantum Theory (without quantization rules), and the whole Physics---including space-time and relativity---is emergent from the processing. And, since Quantum Theory itself is made with purely informational principles, the whole Physics must be reformulated in information-theoretical terms. Here's the TOC of the talk: a) Very short review of the informational axiomatization of Quantum Theory; b) How space-time and relativistic covariance emerge from the quantum computation; c) Special relativity without space: other ideas; d) Dirac equation derived as information flow (without the need of Lorentz covariance); e) Information-theoretical meaning of inertial mass and Planck constant; f) Observable consequences (at the Planck scale?); h) What about Gravity? Three alternatives as a start for a brainstorming. Giacomo D'Ariano http://streamer.perimeterinstitute.ca/mp3/49b1a746-2a88-4a2e-8e1c-4d3b31a5c199.mp3 Science http://streamer.perimeterinstitute.ca/mp3/49b1a746-2a88-4a2e-8e1c-4d3b31a5c199.mp3 Tue, 30 Nov 2010 16:00:00 -0500 A picture can be used to represent an experiment. In this talk we will consider such pictures and show how to turn them into pictures representing calculations (in the style of Penrose's diagrammatic tensor notation). In particular, we will consider circuits described probabilistically. A circuit represents an experiment where we act on various systems with boxes, these boxes being connected by the passage of systems between them. We will make two assumptions concerning such circuits. These two assumptions allow us to set up the duotensor framework (a duotensor is like a tensor except that each position is associated with two possible bases). We will see that quantum theory can be formulated in this framework. Each of the usual objects of quantum theory (states, measurements, transformations) are special cases of duotensors. The framework is motivated by the objective of providing a formulation of quantum theory which is local in the sense that, in doing a calculation pertaining to a particular region of spacetime, we need only use mathematical objects that pertain to this same region. This is, I argue, a prerequisite in a theory of quantum gravity. Reference for this talk: http://arxiv.org/abs/1005.5164 Lucien Hardy http://streamer.perimeterinstitute.ca/mp3/ce720d99-48e4-4573-a3fe-6be9c0ed97c5.mp3 Science http://streamer.perimeterinstitute.ca/mp3/ce720d99-48e4-4573-a3fe-6be9c0ed97c5.mp3 Tue, 07 Dec 2010 16:00:00 -0500 Nonlocality is arguably one of the most remarkable features of quantum mechanics. On the other hand nature seems to forbid other no-signaling correlations that cannot be generated by quantum systems. Usual approaches to explain this limitation is based on information theoretic properties of the correlations without any reference to physical theories they might emerge from. However, as shown in [PRL 104, 140401 (2010)], it is the structure of local quantum systems that determines the bipartite correlations possible in quantum mechanics. We investigate this connection further by introducing toy systems with regular polygons as local state spaces. This allows us to study the transition between bipartite classical, no-signaling and quantum correlations by modifying only the local state space. It turns out that the strength of nonlocality of the maximally entangled state depends crucially on a simple geometric property of the local state space, known as strong self-duality. We prove that the limitation of nonlocal correlations is a general result valid for the maximally entangled state in any model with strongly self-dual local state spaces, since such correlations must satisfy the principle of macroscopic locality. This implies notably that Tsirelson&Atilde;&cent;&Acirc;€&Acirc;™s bound for correlations of the maximally entangled state in quantum mechanics can be regarded as a consequence of strong self-duality of local quantum systems. Finally, our results also show that there exist models which are locally almost identical to quantum mechanics, but can nevertheless generate maximally nonlocal correlations. Peter Janotta http://streamer.perimeterinstitute.ca/mp3/cacc0076-497d-4f4b-b280-a93357d09b0c.mp3 Science http://streamer.perimeterinstitute.ca/mp3/cacc0076-497d-4f4b-b280-a93357d09b0c.mp3 Tue, 14 Dec 2010 16:00:00 -0500 Quantum mechanics does not allow us to measure all possible combinations of observables on one system. Even in the simplest case of two observables we know, that measuring one of the observables changes the system in such way, that the other measurement will not give us desired precise information about the state of the system. Prominent examples of such observables are measurement of position and momentum of a particle, or measuring spin along two orthogonal directions. However, once we accept the possibility of imprecise measurements, we can consider to perform such measurement within one experiment. This is the basis of the notion of coexistence. I will present the basics of coexistence by showing how to perform the spin measurement in two directions, while considering the imprecision of the measurement described by POVMs. We can also go a little further and consider coexistence of instruments, i.e. measurements, where on the output besides classical information we are also left out with quantum post-measurement state. Daniel Reitzner http://streamer.perimeterinstitute.ca/mp3/fe6b3301-5078-4dde-9c4b-21b743022c31.mp3 Science http://streamer.perimeterinstitute.ca/mp3/fe6b3301-5078-4dde-9c4b-21b743022c31.mp3 Mon, 24 Jan 2011 14:00:00 -0500 Symmetric monoidal categories provide a convenient and enlightening framework within which to compare and contrast physical theories on a common mathematical footing. In this talk we consider two theories: stabiliser qubit quantum mechanics and the toy bit theory proposed by Rob Spekkens. Expressed in the categorical framework the two theories look very similar mathematically, reflecting their common physical features. There are differences though: in particular a finite Abelian group emerges naturally in the categorical framework, and this group is different in each case ($Z_4$ for the stabiliser theory and $Z_2 times Z_2$ for the toy bit theory). It turns out that this mathematical difference corresponds directly with a key physical difference between the theories: the stabiliser theory cannot be modelled by local hidden variables, while the toy bit theory can. This analysis can be extended to other Abelian groups yielding a group-theoretic criterion for determining the possibility of local hidden variable interpretations for other physical theories. William Edwards http://streamer.perimeterinstitute.ca/mp3/255d7e54-29ae-4617-a58b-350a4156a183.mp3 Science http://streamer.perimeterinstitute.ca/mp3/255d7e54-29ae-4617-a58b-350a4156a183.mp3 Tue, 25 Jan 2011 16:00:00 -0500 Recently rediscovered results in the theory of partial differential equations show that for free fields, the properties of the field in an arbitrarily small volume of space, traced through eternity, determine completely the field everywhere at all times. Over finite times, the field is determined in the entire region spanned by the intersection of the future null cone of the earliest event and the past null cone of the latest event. Thus this paradigm of classical field theory exhibits a fascinating form of nonlocality. I'll discuss this result and what it tells us about the possibility of constructing a classical, nonlocal theory which accommodates all the phenomena we observe. Steve Weinstein http://streamer.perimeterinstitute.ca/mp3/7b43b70f-c8e2-4ec0-a0b0-3de820fc5063.mp3 Science http://streamer.perimeterinstitute.ca/mp3/7b43b70f-c8e2-4ec0-a0b0-3de820fc5063.mp3 Fri, 04 Feb 2011 13:00:00 -0500 The nature of antimatter is examined in the context of algebraic quantum field theory. It is shown that the notion of antimatter is more general than that of antiparticles. Properly speaking, then, antimatter is not matter made up of antiparticles --- rather, antiparticles are particles made up of antimatter. We go on to discuss whether the notion of antimatter is itself completely general in quantum field theory. Does the matter-antimatter distinction apply to all field theoretic systems? The answer depends on which of several possible criteria we should impose on the space of physical states. Dave Baker http://streamer.perimeterinstitute.ca/mp3/3ba27ef6-0748-4da7-a778-e78176e113ba.mp3 Science http://streamer.perimeterinstitute.ca/mp3/3ba27ef6-0748-4da7-a778-e78176e113ba.mp3 Tue, 01 Mar 2011 16:00:00 -0500 We present a new formulation of quantum mechanics for closed systems like the universe using an extension of familiar probability theory that incorporates negative probabilities. Probabilities must be positive for alternative histories that are the basis of settleable bets. However, quantum mechanics describes alternative histories are not the basis for settleable bets as in the two-slit experiment. These alternatives can be assigned extended probabilities that are sometimes negative. We will compare this with the decoherent (consistent) histories formulation of quantum theory. The prospects for using this formulation as a starting point for testable alternatives to quantum theory or further generalizations of it will be briefly discussed. James Hartle http://streamer.perimeterinstitute.ca/mp3/6fc2ffeb-baa3-4371-9daa-a443b69322b2.mp3 Science http://streamer.perimeterinstitute.ca/mp3/6fc2ffeb-baa3-4371-9daa-a443b69322b2.mp3 Mon, 07 Mar 2011 11:00:00 -0500 Usually, quantum theory (QT) is introduced by giving a list of abstract mathematical postulates, including the Hilbert space formalism and the Born rule. Even though the result is mathematically sound and in perfect agreement with experiment, there remains the question of why this formalism is a natural choice, and how QT could possibly be modified in a consistent way. My talk is on recent work with Lluis Masanes, where we show that five simple operational axioms actually determine the formalism of QT uniquely. This is based to a large extent on Lucien Hardy's seminal work. We start with the framework of &quot;general probabilistic theories&quot;, a simple, minimal mathematical description for outcome probabilities of measurements. Then, we use group theory and convex geometry to show that the state space of a bit must be a 3D (Bloch) ball, finally recovering the Hilbert space formalism. There will also be some speculation on how to find natural post-quantum theories by dropping one of the axioms. Markus Mueller http://streamer.perimeterinstitute.ca/mp3/3c6daa76-b753-4f2d-a50f-fbc17f08ddf2.mp3 Science http://streamer.perimeterinstitute.ca/mp3/3c6daa76-b753-4f2d-a50f-fbc17f08ddf2.mp3 Tue, 15 Mar 2011 16:00:00 -0400 I consider systems that consist of a few hot and a few cold two-level systems and define heat engines as unitaries that extract energy. These unitaries perform logical operations whose complexity depends on both the desired efficiency and the temperature quotient. I show cases where the optimal heat engine solves a hard computational task (e.g. an NP-hard problem) [2]. Heat engines can also drive refrigerators and use the temperature difference between two systems for cooling a third one. I argue that these triples of systems define a classification of thermodynamic resources [1]. All the above assumes that unitaries are implemented by an external controller. To get a thermodynamically reversible process, the joint process on system and controller must be reversible. Then, the implementation of the joint process requires a &quot;meta-controller&quot;, and so on. To study thermodynamic limits without such an infinite sequence of controllers, I introduce the model of &quot;physically universal cellular automata&quot;, in which the boundary between system and controller can be shifted (in analogy to the Heisenberg-cut for the quantum measurement problem). I show that this model raises a lot of fundamental questions [3]. Literature: [1] Janzing et al: Thermodynamic cost of reliability and low temperatures: Tightening Landauer's principle and the second law, J. Stat. Phys. 2000 [2] Janzing: On the computation power of molecular heat engines, J. Stat. Phys. 2006 [3] Janzing: Is there a physically universal cellular automaton or Hamiltonian? arXiv:1009.1720 Dominik Janzing http://streamer.perimeterinstitute.ca/mp3/f70091ac-f4c5-4afa-96cc-608c6ebb9b30.mp3 Science http://streamer.perimeterinstitute.ca/mp3/f70091ac-f4c5-4afa-96cc-608c6ebb9b30.mp3 Thu, 31 Mar 2011 11:00:00 -0400 Ideal measurements are described in quantum mechanics textbooks by two postulates: the collapse of the wave packet and Born&Atilde;&cent;&Acirc;€&Acirc;™s rule for the probabilities of outcomes. The quantum evolution of a system then has two components: a unitary (Hamiltonian) evolution in between measurements and non-unitary one when a measurement is performed. This situation was considered to be unsatisfactory by many people, including Einstein, Bohr, de Broglie, von Neumann and Wigner, but has remained unsolved to date. The quantum measurement problem, that is, understanding why a unique outcome is obtained in each individual run of an experiment, is tackled by solving a Hamiltonian model within standard quantum statistical mechanics. The model describes the measurement of the z-component of a spin through interaction with a magnetic memory. The latter apparatus is modeled by a Curie&Atilde;&cent;&Acirc;€&Acirc;“Weiss magnet having N &Atilde;&cent;&Acirc;‰&Acirc;&laquo; 1 spins weakly coupled to a phonon bath. The Hamiltonian evolution exhibits several time scales. The reduction, a rapid decay of the off-diagonal blocks of the system&Atilde;&cent;&Acirc;€&Acirc;“apparatus density matrix, arises from the many degrees of freedom of the pointer (the magnetization). The registration occurs due to a phase transition from the initial metastable state to one of the final stable states triggered by the tested system. It yields a stationary state in which the apparatus and the system are correlated. Under proper conditions the process satisfies all the features of ideal measurements, including collapse and Born&Atilde;&cent;&Acirc;€&Acirc;™s rule. As usual, irreversibility is ensured by the macroscopic size of the apparatus, in particular by the large value of N. Nothing else than the usual quantum statistical mechanics and Schro &Atilde;Œ&Acirc;ˆdinger equation is needed, and the results support a specified version of the statistical interpretation. The solution of the quantum measurement problem requires a combination of the reduction and the registration, the properties of which arise from the irreversible dynamics. Theo Nieuwenhuizen http://streamer.perimeterinstitute.ca/mp3/420f1800-644b-4d61-b770-fea0a3e457bc.mp3 Science http://streamer.perimeterinstitute.ca/mp3/420f1800-644b-4d61-b770-fea0a3e457bc.mp3 Tue, 12 Apr 2011 16:00:00 -0400 We begin with a fundamental approach to quantum mechanics based on the unitary representations of the group of diffeomorphisms of physical space (and correspondingly, self-adjoint representations of a local current algebra). From these, various classes of quantum configuration spaces arise naturally. One obtains in addition the usual exchange statistics for spatial dimension d &gt;2, induced by representations of the symmetric group, while for d = 2, the approach led to an early prediction of intermediate or &Atilde;&cent;&Acirc;€&Acirc;œanyonic&Atilde;&cent;&Acirc;€&Acirc; statistics induced by unitary representations of the braid group. After reviewing these ideas, which are based on joint work with R. Menikoff and D. H. Sharp at Los Alamos National Laboratory, we shall discuss briefly some analogous possibilities for infinite-dimensional configuration spaces, including anyonic statistics for extended objects in 3-dimensional space. Gerald Goldin http://streamer.perimeterinstitute.ca/mp3/ab087cba-6b92-42b6-887a-a110fc48be1e.mp3 Science http://streamer.perimeterinstitute.ca/mp3/ab087cba-6b92-42b6-887a-a110fc48be1e.mp3 Tue, 26 Apr 2011 16:00:00 -0400 A new ensemble interpretation of quantum mechanics is proposed according to which the ensemble associated to a quantum state really exists: it is the ensemble of all the systems in the same quantum state in the universe. Individual systems within the ensemble have microscopic states, described by beables. The probabilities of quantum theory turn out to be just ordinary relative frequencies probabilities in these ensembles. Laws for the evolution of the beables of individual systems are given such that their ensemble relative frequencies evolve in a way that reproduces the predictions of quantum mechanics. These laws are highly non-local and involve a new kind of interaction between the members of an ensemble that define a quantum state. These include a stochastic process by which individual systems copy the beables of other systems in the ensembles of which they are a member. The probabilities for these copy processes do not depend on where the systems are in space, but do depend on the distribution of beables in the ensemble. Macroscopic systems then are distinguished by being large and complex enough that they have no copies in the universe. They then cannot evolve by the copy law, and hence do not evolve stochastically according to quantum dynamics. This implies novel departures from quantum mechanics for systems in quantum states that can be expected to have few copies in the universe. At the same time, we are able to argue that the centre of masses of large macroscopic systems do satisfy Newton's laws. Lee Smolin http://streamer.perimeterinstitute.ca/mp3/0b0491de-2813-43bc-88a7-5f85221faf8c.mp3 Science http://streamer.perimeterinstitute.ca/mp3/0b0491de-2813-43bc-88a7-5f85221faf8c.mp3 Tue, 03 May 2011 16:00:00 -0400 We will analyze different aspects of locality in causal operational probabilistic theories. We will first discuss the notion of local state and local objective information in operational probabilistic theories, and define an operational notion of discord that coincides with quantum discord in the case of quantum theory. Using such notion, we will show that the only theory in which all separable states have null discord is the classical one. We will then analyze locality of transformations, reviewing some general properties of no-signaling channels in causal theories. We will show that it is natural to define transformations on no-signaling channels that cannot be extended to all bipartite channels, and discuss the consequences of this fact on information processing. Paolo Perinotti http://streamer.perimeterinstitute.ca/mp3/b4960090-3f7b-4c07-bd20-ddb9c0ebb115.mp3 Science http://streamer.perimeterinstitute.ca/mp3/b4960090-3f7b-4c07-bd20-ddb9c0ebb115.mp3 Tue, 17 May 2011 15:00:00 -0400 Quantum theory can be thought of a noncommutative generalization of classical probability and, from this perspective, it is puzzling that no quantum generalization of conditional probability is in widespread use. In this talk, I discuss one such generalization and show how it can unify the description of ensemble preparations of quantum states, POVM measurements and the description of correlations between quantum systems. The conditional states formalism allows for a description of prepare-and-measure experiments that is neutral with respect to the direction of inference, such that both the retrodictive formalism and the more usual predictive formalism are consequences of a more fundamental description in terms of a conditionally independent tripartite state, and the two formalisms are related by a quantum generalization of Bayes' rule. As an application, I give a generalized argument for the pooling rule proposed by Spekkens and Wiseman that is a direct analog of a result in classical supra-Bayesian pooling. Matthew Leifer http://streamer.perimeterinstitute.ca/mp3/ad0d4681-cc88-448f-b673-f7af0850a0c3.mp3 Science http://streamer.perimeterinstitute.ca/mp3/ad0d4681-cc88-448f-b673-f7af0850a0c3.mp3 Tue, 17 May 2011 16:00:00 -0400 I provide a reformulation of finite dimensional quantum theory in the circuit framework in terms of mathematical axioms, and a reconstruction of quantum theory from operational postulates. The mathematical axioms for quantum theory are the following: [Axiom 1] Operations correspond to operators. [Axiom 2] Every complete set of positive operators corresponds to a complete set of operations. The following operational postulates are shown to be equivalent to these mathematical axioms: [P1] Definiteness. Associated with any given pure state is a unique maximal effect giving probability equal to one. This maximal effect does not give probability equal to one for any other pure state. [P2] Information locality. A maximal measurement on a composite system is effected if we perform maximal measurements on each of the components. [P3] Tomographic locality. The state of a composite system can be determined from the statistics collected by making measurements on the components. [P4] Compound permutatability. There exists a compound reversible transformation on any system effecting any given permutation of any given maximal set of distinguishable states for that system. [P5] Preparability. Filters are non-mixing and non-flattening. Hence, from these postulates we can reconstruct all the usual features of quantum theory: States are represented by positive operators, transformations by completely positive trace non-increasing maps, and effects by positive operators. The Born rule (i.e. the trace rule) for calculating probabilities also follows. See arXiv:1104.2066 for more details. These operational postulates are deeper than those I gave ten years ago in quant-ph/0101012. Lucien Hardy http://streamer.perimeterinstitute.ca/mp3/3397cf97-9b24-4d56-9523-93ad6b90c7d4.mp3 Science http://streamer.perimeterinstitute.ca/mp3/3397cf97-9b24-4d56-9523-93ad6b90c7d4.mp3 Wed, 18 May 2011 11:00:00 -0400 This is a geometric tutorial about straight and twisted vectors and forms (ie, de Rham currents) leading to some wild thoughts about the EM field as a *thing*, ie with properties similar to a piece of matter; and to some even wilder thoughts about a metric-free GR. PierGianLuca Porta Mana http://streamer.perimeterinstitute.ca/mp3/2cdaba30-de1c-48ff-bd47-f62cf06de3bb.mp3 Science http://streamer.perimeterinstitute.ca/mp3/2cdaba30-de1c-48ff-bd47-f62cf06de3bb.mp3 Tue, 24 May 2011 16:00:00 -0400 This is a very informal talk about some of the issues associated with the notion of &quot;macroscopic realism&quot; (MR) and its relation to quantum mechanics (QM). After a brief discussion of the motivation for attempts to modify QM at some point between the level of the atom and that of our own direct experience, and a survey of some candidate experimental systems, I will discuss attempts to quantify the notion of &quot;macroscopic distinctness&quot;, the use of temporal Bell inequalities to discriminate between the predictions of QM and those of MR, the related concept of &quot;noninvasive measurement&quot; and existing and possible ways to implement it. I will also comment briefly on the relation between Bell-EPR experiments and those on MR. Sir Anthony Leggett http://streamer.perimeterinstitute.ca/mp3/70e809cf-5e34-4fa7-8357-588c863ad259.mp3 Science http://streamer.perimeterinstitute.ca/mp3/70e809cf-5e34-4fa7-8357-588c863ad259.mp3 Tue, 19 Jul 2011 14:00:00 -0400 Yakir Aharonov http://streamer.perimeterinstitute.ca/mp3/d10d140b-0575-4707-a75d-65e810c8f238.mp3 Science http://streamer.perimeterinstitute.ca/mp3/d10d140b-0575-4707-a75d-65e810c8f238.mp3 Tue, 23 Aug 2011 11:00:00 -0400 Wheeler's delayed choice (WDC) is one of the &quot;standard experiments in foundations&quot;. It aims at the puzzle of a photon simultaneously behaving as wave and particle. Bohr-Einstein debate on wave-particle duality prompted the introduction of Bohr's principle of complementarity, ---`.. the study of complementary phenomena demands mutually exclusive experimental arrangements&quot; . In WDC experiment the mutually exclusive setups correspond to the presence or absence of a second beamsplitter in a Mach-Zehnder interferometer (MZI). A choice of the setup determines the observed behaviour. The delay ensures that the behaviour cannot be adapted before the photon enters MZI. Using WDC as an example, we show how replacement of classical selectors by quantum gates streamlines experiments and impacts on foundational questions. We demonstrate measurements of complementary phenomena with a single setup, where observed behaviour of the photon is chosen after it has been already detected. Spacelike separation of the setup components becomes redundant. The complementarity principle has to be reformulated --- instead of complementarity of experimental setups we now have complementarity of measurement results. Finally we present a quantum-controlled scheme of Bell-type experiments. To reach any of these conclusions in either classical or quantum setting a (simple) hidden variable model that represents the &quot;reality&quot; of &quot;particle&quot; and &quot;wave&quot; should be analyzed. The model is never fully exorcised but just pushed to have more and more conspiratorial set of assumptions. Daniel Terno http://streamer2.perimeterinstitute.ca/mp3/11090124.mp3 Science http://streamer2.perimeterinstitute.ca/mp3/11090124.mp3 Tue, 27 Sep 2011 16:00:00 -0400 A family of probability distributions (i.e. a statistical model) is said to be sufficient for another, if there exists a transition matrix transforming the probability distributions in the former to the probability distributions in the latter. The so-called Blackwell-Sherman-Stein Theorem provides necessary and sufficient conditions for one statistical model to be sufficient for another, by comparing their &quot;information values&quot; in a game-theoretical framework. In this talk, I will extend some of these ideas to the quantum case. I will begin by considering the comparison of ensembles of quantum states in terms of their &quot;information value&quot; in quantum statistical decision problems. In this case, I will prove that one ensemble is &quot;more informative&quot; than another if and only if there exists a suitable processing of the former into the latter. I will then move on to the comparison of bipartite quantum states in terms of their &quot;nonlocality value&quot; in nonlocal games. In this case, I will prove that one bipartite state is &quot;more nonlocal&quot; than another if and only if the former can be transformed into the latter by local operations and shared randomness, arguing, moreover, that the framework provided by nonlocal games can be useful in understanding analogies and differences between the notions of quantum entanglement and nonlocality. Francesco Buscemi http://streamer2.perimeterinstitute.ca/mp3/11100065.mp3 Science http://streamer2.perimeterinstitute.ca/mp3/11100065.mp3 Tue, 04 Oct 2011 16:00:00 -0400 Classical constraints come in various forms: first and second class, irreducible and reducible, regular and irregular, all of which will be illustrated. They can lead to severe complications when classical constraints are quantized. An additional complication involves whether one should quantize first and reduce second or vice versa, which may conflict with the axiom that canonical quantization requires Cartesian coordinates. Most constraint quantization procedures (e.g., Dirac, BRST, Faddeev) run into difficulties with some of these issues and may lead to erroneous results. The Projection Operator Method involves no gauge fixing, no auxiliary variables of any kind, and can treat simultaneously any and all kinds of constraints. It also admits a phase space path integral formulation with similar features. John Klauder http://streamer2.perimeterinstitute.ca/mp3/11100083.mp3 Science http://streamer2.perimeterinstitute.ca/mp3/11100083.mp3 Tue, 11 Oct 2011 15:30:00 -0400 We use the mathematical language of sheaf theory to give a unified treatment of non-locality and contextuality, which generalizes the familiar probability tables used in non-locality theory to cover Kochen-Specker configurations and more. We show that contextuality, and non-locality as a special case, correspond exactly to *obstructions to the existence of global sections*. We describe a linear algebraic approach to computing these obstructions, which allows a systematic treatment of arguments for non-locality and contextuality. A general correspondence is shown between the existence of local hidden-variable realizations using negative probabilities, and no-signalling. Maximal non-locality is generalized to maximal contextuality, and characterized in purely qualitative terms, as the non-existence of global sections in the support. Some ongoing work with Shane Mansfield and Rui Soares Barbosa is described, which identifies *cohomological obstructions* to the existence of global sections, opening the possibility of applying the powerful methods of cohomology to non-locality and contextuality. Samson Abramsky http://streamer2.perimeterinstitute.ca/mp3/11110108.mp3 Science http://streamer2.perimeterinstitute.ca/mp3/11110108.mp3 Tue, 01 Nov 2011 15:30:00 -0400 Quantum theory can be thought of as a noncommutative generalization of Bayesian probability theory, but for the analogy to be convincing, it should be possible to describe inferences among quantum systems in a manner that is independent of the causal relationship between those systems. In particular, it should be possible to unify the treatment of two kinds of inferences: (i) from beliefs about one system to beliefs about another, for instance, in the Einstein-Podolsky-Rosen or &quot;quantum steering&quot; phenomenon, and (ii) from beliefs about a system at one time to beliefs about that same system at another time, for instance, in predictions or retrodictions about a system undergoing dynamical evolution or undergoing a measurement. I will present a formalism that achieves such a unification by making use of &quot;conditional quantum states&quot;, a noncommutative generalization of conditional probabilities. I argue for causal neutrality by drawing a comparison with a classical statistical theory with an epistemic restriction. (Joint work with Matthew Leifer). Robert Spekkens http://streamer2.perimeterinstitute.ca/mp3/11110114.mp3 Science http://streamer2.perimeterinstitute.ca/mp3/11110114.mp3 Tue, 08 Nov 2011 15:30:00 -0500 It is my contention that non-commutative geometry is really "ordinary geometry" carried out in a non-commutative logic. I will sketch a specific project, relating groupoid C*-algebras to toposes, by means of which I hope to detect the nature of this non-commutative logic. Jeff Egger http://streamer2.perimeterinstitute.ca/mp3/11110124.mp3 Science http://streamer2.perimeterinstitute.ca/mp3/11110124.mp3 Thu, 24 Nov 2011 10:30:00 -0500 The experimental violation of Bell inequalities using spacelike separated measurements precludes the explanation of quantum correlations through causal influences propagating at subluminal speed. Yet, it is always possible, in principle, to explain such experimental violations through models based on hidden influences propagating at a finite speed v>c, provided v is large enough. Here, we show that for any finite speed v>c, such models predict correlations that can be exploited for faster-than-light communication. This superluminal communication does not require access to any hidden physical quantities, but only the manipulation of measurement devices at the level of our present-day description of quantum experiments. Hence, assuming the impossibility of using quantum non-locality for superluminal communication, we exclude any possible explanation of quantum correlations in term of finite-speed influences. Jean-Daniel Bancal http://streamer2.perimeterinstitute.ca/mp3/11110145.mp3 Science http://streamer2.perimeterinstitute.ca/mp3/11110145.mp3 Tue, 29 Nov 2011 15:30:00 -0500 Jonathan Oppenheim http://streamer2.perimeterinstitute.ca/mp3/11120040.mp3 Science http://streamer2.perimeterinstitute.ca/mp3/11120040.mp3 Wed, 07 Dec 2011 14:00:00 -0500 We prove an uncertainty relation for energy and arrival time, where the arrival of a particle at a detector is modeled by an absorbing term added to the Hamiltonian. In this well-known scheme the probability for the particle's arrival at the counter is identified with the loss of normalization for an initial wave packet. The result is obtained under the sole assumption that the absorbing term vanishes on the initial wave function. Nearly minimal uncertainty can be achieved in a two-level system. Jukka Kiukas http://streamer2.perimeterinstitute.ca/mp3/12010145.mp3 Science http://streamer2.perimeterinstitute.ca/mp3/12010145.mp3 Tue, 17 Jan 2012 15:30:00 -0500 Categorical quantum mechanics (CQM) uses symmetric monoidal categories to formalize quantum theory, in order to extract the key structures that yield protocols such as teleportation in an abstract way. This formalism admits a purely graphical calculus, but the causal structure of these diagrams, and the formalism in general, is unclear. We begin by considering the signaling abilities of probabilistic devices with inputs and outputs and we show how a non-signaling device can become a perfect signaling device under time-reversal. This conflicts with the causal structure of relativity, and suggests that an `asymmetry' is needed when formalizing causality in CQM. We then show how a fixed causal structure within CQM corresponds to topological connectedness in the graphical language, and that correlations, either classical or quantum, force terminality of the tensor unit. We also show that well-definedness of a global state forces the monoidal product to be only partially defined, which in turn results in a covariance theorem. These structural results lead to a mathematical entity which we call a `causal category'. Raymond Lal http://streamer2.perimeterinstitute.ca/mp3/12010157.mp3 Science http://streamer2.perimeterinstitute.ca/mp3/12010157.mp3 Thu, 26 Jan 2012 15:00:00 -0500 We present a quantization method based on theEhrenfest theorem embedded in an extended algebraic structure capableof consistently describing hybrid quantum-classical systems, where thestandard quantum and classical mechanics are two limiting cases. TheWigner phase space formulation and the Schordinger equation are foundto be two alternative representations of the quantum case while theKoopman-von Neumann equation is the corresponding classicalcounterpart. Moreover, the developed quantization procedure isgeneralized to describe open systems, quantum/classical field theoriesand relativistic mechanics where new dynamical equations appear,shedding new light on important practical problems such asunderstanding of the quantum/classical transition and modeling ofmesoscopic systems.

Related references: arXiv:1105.4014, arXiv:1112.3679, arXiv:1107.5139 Denys Bondar http://streamer2.perimeterinstitute.ca/mp3/12010167.mp3 Science http://streamer2.perimeterinstitute.ca/mp3/12010167.mp3 Tue, 31 Jan 2012 15:30:00 -0500 The standard approach to quantum nonlocality (Bell's Theorem) relies on the assumption of the existence of "free will". I will explain how to get rid of this mysterious assumption in favor of the independence of sources. From this new point of view, Bell's Theorem becomes a statement about Bayesian networks. Besides allowing a more intuitive formulation of the standard result, our formalism also provides new network topologies giving rise to new kinds of nonlocality. Some of these relate to results by Steudel and Ay on the statistical inference of causal relations. Witnessing quantum nonlocality in new network topologies is a challenge which I will pose as an open problem. Tobias Fritz http://streamer2.perimeterinstitute.ca/mp3/12020134.mp3 Science http://streamer2.perimeterinstitute.ca/mp3/12020134.mp3 Tue, 07 Feb 2012 15:30:00 -0500