Gleason’s theorem for composite systems

DOI10.1088/1751-8121/acfbcbarXiv2205.00493MaRDI QIDQ6060193

Andreas Döring, Unnamed Author

Publication date: 3 November 2023

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2205.00493

zbMATH Keywords

von Neumann algebrasquantum correlationsquantum foundationsGleason's theoremStinespring dilation

Mathematics Subject Classification ID

Measures of association (correlation, canonical correlation, etc.) (62H20) Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product) (46C05) General and philosophical questions in quantum theory (81P05) General theory of von Neumann algebras (46L10) Quantum measurement theory, state operations, state preparations (81P15) General theory of linear incidence geometry and projective geometries (51A05)

Cites Work

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• Bohrification of operator algebras and quantum logic
• Dye's theorem and Gleason's theorem for \(AW^\ast\)-algebras
• Quantum measurement
• A topos for algebraic quantum theory
• Quantum measures and states on Jordan algebras
• A Radon-Nikodym theorem for completely positive maps
• Tensor products and probability weights
• A factor not anti-isomorphic to itself
• Completely positive linear maps on complex matrices
• On orientation and dynamics in operator algebras. I
• Topos perspective on the Kochen-Specker theorem. I: Quantum states as generalized valuations
• A taste of Jordan algebras
• Topos perspective on the Kochen-Specker theorem. III: Von Neumann algebras as the base category.
• Topos perspective on the Kochen--Specker theorem. IV: Interval valuations
• On Dye's theorem for Jordan operator algebras
• A topos perspective on the Kochen-Specker theorem. II: Conceptual aspects and classical analogues
• Measures on projections and physical states
• Operator algebras. Theory of \(C^*\)-algebras and von Neumann algebras
• Kochen-Specker theorem for von Neumann algebras
• “What is a Thing?”: Topos Theory in the Foundations of Physics
• Decomposable Positive Maps on C ∗ -Algebras
• Measures on Projections in W*-algebras of Type II₁
• Finitely Additive Measures on Projections in Finite W^* -Algebras
• Orientation in operator algebras
• The Mackey-Gleason Problem
• Duality of observables and generators in classical and quantum mechnics
• The analogue of Choi matrices for a class of linear maps on Von Neumann algebras
• Getting to the Bottom of Noether’s Theorem
• Informational axioms for quantum theory
• A topos foundation for theories of physics: I. Formal languages for physics
• A topos foundation for theories of physics: II. Daseinisation and the liberation of quantum theory
• A topos foundation for theories of physics: III. The representation of physical quantities with arrows δ̆o(A):Σ̱→R≽̱
• A topos foundation for theories of physics: IV. Categories of systems
• An Algebraic Approach to Quantum Field Theory
• On the Problem of Hidden Variables in Quantum Mechanics
• PROBABILITY MEASURES ON PROJECTIONS IN VON NEUMANN ALGEBRAS
• Positive Functions on C ∗ -Algebras
• Contextuality and the fundamental theorems of quantum mechanics
• Information and the Reconstruction of Quantum Physics

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