Synchronous correlation matrices and Connes’ embedding conjecture

DOI10.1063/1.4936751zbMath1330.81027arXiv1503.07207OpenAlexW3098935089WikidataQ122901903 ScholiaQ122901903MaRDI QIDQ2786619

Vern I. Paulsen, Kenneth J. Dykema

Publication date: 15 February 2016

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

Full work available at URL: https://arxiv.org/abs/1503.07207

Mathematics Subject Classification ID

General and philosophical questions in quantum theory (81P05) Operator spaces and completely bounded maps (46L07) General theory of (C^*)-algebras (46L05) Applications of selfadjoint operator algebras to physics (46L60) Coloring of graphs and hypergraphs (05C15)

Related Items (12)

Bounds on entanglement dimensions and quantum graph parameters via noncommutative polynomial optimization ⋮ Additivity violation of the regularized minimum output entropy ⋮ Quantum hypergraph homomorphisms and non-local games ⋮ THE SET OF QUANTUM CORRELATIONS IS NOT CLOSED ⋮ Bisynchronous games and factorizable maps ⋮ Non-closure of the set of quantum correlations via graphs ⋮ Connectivity for quantum graphs ⋮ Geometry of the set of synchronous quantum correlations ⋮ A synchronous game for binary constraint systems ⋮ Linear conic formulations for two-party correlations and values of nonlocal games ⋮ Tsirelson’s problem and an embedding theorem for groups arising from non-local games ⋮ Quantum graph homomorphisms via operator systems

Cites Work

• About the Connes embedding conjecture
• On the quantum chromatic number of a graph
• Classification of injective factors. Cases \(\mathrm{II}_1\), \(\mathrm{II}_\infty\), \(\mathrm{III}_\lambda\), \(\lambda\neq 1\)
• On non-semisplit extensions, tensor products and exactness of group \(C^*\)-algebras
• The analogues of entropy and of Fisher's information measure in free probability theory. II
• Operator systems from discrete groups
• Matrices of unitary moments
• TSIRELSON'S PROBLEM AND KIRCHBERG'S CONJECTURE
• Graph Homomorphisms for Quantum Players
• FREE ENTROPY
• Connes' embedding problem and Tsirelson's problem
• QUANTUM CHROMATIC NUMBERS VIA OPERATOR SYSTEMS
• Kochen–Specker Sets and the Rank-1 Quantum Chromatic Number
• The $C^*$-algebra generated by two projections.
• Estimating quantum chromatic numbers

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