C05010 - Quantum Information, Computation and Logic: Exploring New Connections Both quantum logic (QL) and quantum information (QI) are based on viewing quantum mechanics in terms of concepts closely tied to information, so QL, should be closely connected to QI. On the whole, these two research fields are pursued by separate communities and so a closer collaboration is likely to yield significant insights into both. While taking a broad view of both fields, the workshop will focus on areas that we feel are most likely to spark significant collaboration and new research initiatives. http://pirsa.org/podcast/C05010 Science 2012 http://blogs.law.harvard.edu/tech/rss en-ca Thu, 09 Feb 2012 04:41:42 -0500 sbradwell@perimeterinstitute.ca Thu, 09 Feb 2012 04:41:42 -0500 G 180 pirsa-admin@perimeterinstitute.ca Steve Bradwell's - Podcast Generator Introduction to and Historical Overview of Quantum Logics Introductory lecture summary: 1. Finite dimensional hilbert spaces and (complemented) modular lattices; infinite-dimensional hilbert spaces and orthomodularity. 2. von Neumann's QL; von Neumann-Birkhoff (briefly!); reconstruction of QM from P(H) 3. Mackey's programme; some early axiomatics (e.g., Zierler); QLs as OMPs + order-determining sets of states 4. Piron's Theorem; some discussion of Piron's axioms 5. Keller's examples (maybe just a mention, though I'd like to indicate how they come up); Soler's theorem (just the statement) 6. Abstract OMLs; Greechie Diagrams and the Loop Lemma; brief mention of Harding's results on decompositions 7. Tensor products (the F-R example, showing OMLs not stable under tensor products); orthoalgebras. 8. Orthoalgebras from test spaces Alex Wilce http://streamer.perimeterinstitute.ca/mp3/60c494aa-254a-4651-8ed7-6be696571c51.mp3 Science http://streamer.perimeterinstitute.ca/mp3/60c494aa-254a-4651-8ed7-6be696571c51.mp3 Sun, 17 Jul 2005 14:00:00 -0400 Dynamic and Modal Aspects of Quantum Logic Languages (syntax of modal logic, dynamic logic, epistemic logic). Relational (Kripke) models. Algebraic models (quantales, dynamic algebras). Axioms. Alexandru Baltag http://streamer.perimeterinstitute.ca/mp3/3e70f1da-ce32-41a2-b34e-2065992cc658.mp3 Science http://streamer.perimeterinstitute.ca/mp3/3e70f1da-ce32-41a2-b34e-2065992cc658.mp3 Sun, 17 Jul 2005 15:30:00 -0400 Operational Quantum Logic Introductory lecture summary: Operational Quantum Logic I: Effect Algebras, States, and Basic Convexity • Effect algebras, effect test-spaces, PAS's (partial abelian semigroups). • Morphisms, states, dynamics. Classes of effect algebras whose state-set has nice properties. • Operational derivation of effect algberas, summarized. • "Theories"--- Effect-state systems. • Tensor product (defined, existence result stated). • Some notions of sharpness in EA's, examples that separate them, conditional equivalences that are interesting. • Convex cones/sets, ordered linear space basics. Partially ordered abelian groups. Operational Quantum Logic II: Convexity, Representations, and Operations • Convex cones and convex sets. Extremality. Krein-Milman. Caratheodory. Affine maps. • Positive maps. Automorphisms. Dual space, Dual cone. Adjoint map. Faces. Exposed faces. Lattices of faces. • Interval EA's, representations on partially ordered abelian groups, unigroups. Analogues of Naimark's theorem, open problems. • Convex EA's. Observables, "generalized" observables. Representation theorem for convex EA's. Relation of observables to effects formulation. • State representation theorem for finite-d homogeneous self-dual cones (statement). • Homogeneous cones as slices of positive semidefinite cones (statement). • Axioms concerning the face lattice. Howard Barnum http://streamer.perimeterinstitute.ca/mp3/6a2dca6b-734a-45d0-b3ae-a2a2c4631585.mp3 Science http://streamer.perimeterinstitute.ca/mp3/6a2dca6b-734a-45d0-b3ae-a2a2c4631585.mp3 Sun, 17 Jul 2005 16:30:00 -0400 Operational Quantum Logic Introductory lecture summary: Operational Quantum Logic I: Effect Algebras, States, and Basic Convexity • Effect algebras, effect test-spaces, PAS's (partial abelian semigroups). • Morphisms, states, dynamics. Classes of effect algebras whose state-set has nice properties. • Operational derivation of effect algberas, summarized. • "Theories"--- Effect-state systems. • Tensor product (defined, existence result stated). • Some notions of sharpness in EA's, examples that separate them, conditional equivalences that are interesting. • Convex cones/sets, ordered linear space basics. Partially ordered abelian groups. Operational Quantum Logic II: Convexity, Representations, and Operations • Convex cones and convex sets. Extremality. Krein-Milman. Caratheodory. Affine maps. • Positive maps. Automorphisms. Dual space, Dual cone. Adjoint map. Faces. Exposed faces. Lattices of faces. • Interval EA's, representations on partially ordered abelian groups, unigroups. Analogues of Naimark's theorem, open problems. • Convex EA's. Observables, "generalized" observables. Representation theorem for convex EA's. Relation of observables to effects formulation. • State representation theorem for finite-d homogeneous self-dual cones (statement). • Homogeneous cones as slices of positive semidefinite cones (statement). • Axioms concerning the face lattice Howard Barnum http://streamer.perimeterinstitute.ca/mp3/0cce61d0-03dd-483d-8129-3df31eb683e7.mp3 Science http://streamer.perimeterinstitute.ca/mp3/0cce61d0-03dd-483d-8129-3df31eb683e7.mp3 Mon, 18 Jul 2005 15:30:00 -0400 July 18, 2005 - TBA Sonjas Smets,Alexandru Baltag http://streamer.perimeterinstitute.ca/mp3/efd51d4e-cb00-49e3-af26-9b5f2735588f.mp3 Science http://streamer.perimeterinstitute.ca/mp3/efd51d4e-cb00-49e3-af26-9b5f2735588f.mp3 Mon, 18 Jul 2005 16:30:00 -0400 Introduction to logics as type theories for quantum processes Samson Abramsky http://streamer.perimeterinstitute.ca/mp3/f92198bf-fd67-4ce8-8e98-90bc67031c48.mp3 Science http://streamer.perimeterinstitute.ca/mp3/f92198bf-fd67-4ce8-8e98-90bc67031c48.mp3 Tue, 19 Jul 2005 11:00:00 -0400 Preparation contextuality in its myriad forms Robert Spekkens http://streamer.perimeterinstitute.ca/mp3/e39f3961-601f-435d-a9de-e5751b0c8485.mp3 Science http://streamer.perimeterinstitute.ca/mp3/e39f3961-601f-435d-a9de-e5751b0c8485.mp3 Tue, 19 Jul 2005 14:00:00 -0400 Information is physical, but physics is logical Samson Abramsky http://streamer.perimeterinstitute.ca/mp3/a478c441-29d9-47c6-ba9b-fa3833b2b75a.mp3 Science http://streamer.perimeterinstitute.ca/mp3/a478c441-29d9-47c6-ba9b-fa3833b2b75a.mp3 Tue, 19 Jul 2005 14:45:00 -0400 Nondeterministic testing of sequential quantum logic propositions on a quantum computer Matthew Leifer http://streamer.perimeterinstitute.ca/mp3/a1ea0bb7-93b5-46d1-a751-c6596f665cc9.mp3 Science http://streamer.perimeterinstitute.ca/mp3/a1ea0bb7-93b5-46d1-a751-c6596f665cc9.mp3 Tue, 19 Jul 2005 16:00:00 -0400 The logic of quantum actions: reasoning about change in quantum systems Sonja Smets http://streamer.perimeterinstitute.ca/mp3/459bacea-911a-4e67-9350-42a763aa1009.mp3 Science http://streamer.perimeterinstitute.ca/mp3/459bacea-911a-4e67-9350-42a763aa1009.mp3 Tue, 19 Jul 2005 16:45:00 -0400 Symmetry and quantum logic Alex Wilce http://streamer.perimeterinstitute.ca/mp3/baacefa4-adaa-49a5-b38e-df81f6d54a44.mp3 Science http://streamer.perimeterinstitute.ca/mp3/baacefa4-adaa-49a5-b38e-df81f6d54a44.mp3 Wed, 20 Jul 2005 09:30:00 -0400 Discrete phase space based on finite fields William Wootters http://streamer.perimeterinstitute.ca/mp3/c18cea9b-6ebe-4a55-bc5f-9e493697f7fb.mp3 Science http://streamer.perimeterinstitute.ca/mp3/c18cea9b-6ebe-4a55-bc5f-9e493697f7fb.mp3 Wed, 20 Jul 2005 10:15:00 -0400 Rickart comparability groups and quantum logic David Foulis http://streamer.perimeterinstitute.ca/mp3/cb94cb3c-8899-425a-ac89-8c4c63b1852c.mp3 Science http://streamer.perimeterinstitute.ca/mp3/cb94cb3c-8899-425a-ac89-8c4c63b1852c.mp3 Wed, 20 Jul 2005 11:30:00 -0400 Residuated Mappings Richard Greechie http://streamer.perimeterinstitute.ca/mp3/20acde1d-653c-43c1-998e-bc03c1f608bf.mp3 Science http://streamer.perimeterinstitute.ca/mp3/20acde1d-653c-43c1-998e-bc03c1f608bf.mp3 Wed, 20 Jul 2005 14:00:00 -0400 Are Quantum States Exponentially Long Vectors? Scott Aaronson http://streamer.perimeterinstitute.ca/mp3/b2cbd00a-69f4-41eb-bd04-78a6658820e6.mp3 Science http://streamer.perimeterinstitute.ca/mp3/b2cbd00a-69f4-41eb-bd04-78a6658820e6.mp3 Wed, 20 Jul 2005 16:15:00 -0400 Nonlocal no-signalling correlations that are locally quantum. Howard Barnum http://streamer.perimeterinstitute.ca/mp3/cf92e3cc-10bf-48a9-b9d6-afbd4e2e0dfa.mp3 Science http://streamer.perimeterinstitute.ca/mp3/cf92e3cc-10bf-48a9-b9d6-afbd4e2e0dfa.mp3 Wed, 20 Jul 2005 17:00:00 -0400 What is a quantum computation? Hans Briegel http://streamer.perimeterinstitute.ca/mp3/44cb282e-8fb7-4c52-aff0-ac40a3c02e94.mp3 Science http://streamer.perimeterinstitute.ca/mp3/44cb282e-8fb7-4c52-aff0-ac40a3c02e94.mp3 Thu, 21 Jul 2005 09:30:00 -0400 Quantum algorithm and measurement based models of computation. Richard Jozsa http://streamer.perimeterinstitute.ca/mp3/e9179fa1-616b-49be-9be6-95cc8a1dd187.mp3 Science http://streamer.perimeterinstitute.ca/mp3/e9179fa1-616b-49be-9be6-95cc8a1dd187.mp3 Thu, 21 Jul 2005 10:15:00 -0400 Information flow in graph states computing Elham Kashefi http://streamer.perimeterinstitute.ca/mp3/7aa31af5-f8fc-4d42-bea5-aba593c877b3.mp3 Science http://streamer.perimeterinstitute.ca/mp3/7aa31af5-f8fc-4d42-bea5-aba593c877b3.mp3 Thu, 21 Jul 2005 11:30:00 -0400 Generalised Probability Theories as a setting for Quantum Theory and other theories. Lucien Hardy http://streamer.perimeterinstitute.ca/mp3/4c00c9b4-429b-465d-b7ba-da4740713122.mp3 Science http://streamer.perimeterinstitute.ca/mp3/4c00c9b4-429b-465d-b7ba-da4740713122.mp3 Thu, 21 Jul 2005 14:00:00 -0400 Quantum Logics, Spaces of States,Ordered Banach Spaces, and their Connections to the Works of Foulis- Randall, Gunson, Ludwig, Birkhoff- von Neumann ,... Tim Cook http://streamer.perimeterinstitute.ca/mp3/d55acca5-91b7-4a07-a1f6-949b6dc012fa.mp3 Science http://streamer.perimeterinstitute.ca/mp3/d55acca5-91b7-4a07-a1f6-949b6dc012fa.mp3 Thu, 21 Jul 2005 14:45:00 -0400 The Frequency Operator in Quantum Mechanics. Ruediger Schack http://streamer.perimeterinstitute.ca/mp3/fd8fb764-3907-4a80-b073-98073547874e.mp3 Science http://streamer.perimeterinstitute.ca/mp3/fd8fb764-3907-4a80-b073-98073547874e.mp3 Thu, 21 Jul 2005 16:00:00 -0400 A Structure for Quantum Measurements and Observables Stan Gudder http://streamer.perimeterinstitute.ca/mp3/e817b721-e48e-40b1-9686-bc916bcaf0b7.mp3 Science http://streamer.perimeterinstitute.ca/mp3/e817b721-e48e-40b1-9686-bc916bcaf0b7.mp3 Thu, 21 Jul 2005 16:45:00 -0400 Super-quantum correlations and linear dynamics Jonathon Barret http://streamer.perimeterinstitute.ca/mp3/ed62d51f-dea4-4d39-a7b0-13668c635751.mp3 Science http://streamer.perimeterinstitute.ca/mp3/ed62d51f-dea4-4d39-a7b0-13668c635751.mp3 Fri, 22 Jul 2005 10:15:00 -0400 Kindergarten quantum mechanics Bob Coecke http://streamer.perimeterinstitute.ca/mp3/46b51953-9f00-4c69-9746-2b2264b036ed.mp3 Science http://streamer.perimeterinstitute.ca/mp3/46b51953-9f00-4c69-9746-2b2264b036ed.mp3 Fri, 22 Jul 2005 11:30:00 -0400