Quantum graph homomorphisms via operator systems

DOI10.1016/j.laa.2016.02.019zbMath1353.46041arXiv1505.00483OpenAlexW2963287525MaRDI QIDQ254876

Vern I. Paulsen, Carlos M. Ortiz

Publication date: 8 March 2016

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1505.00483

zbMATH Keywords

graph homomorphismsentangled gamesnon-localityoperator systems

Mathematics Subject Classification ID

Operator spaces and completely bounded maps (46L07) General theory of (C^*)-algebras (46L05) Operator spaces (= matricially normed spaces) (47L25)

Related Items (14)

Bounds on entanglement dimensions and quantum graph parameters via noncommutative polynomial optimization ⋮ Bigalois extensions and the graph isomorphism game ⋮ A compositional approach to quantum functions ⋮ Quantum and non-signalling graph isomorphisms ⋮ \(\mathrm{MIP}^* = \mathrm{RE}\): a negative resolution to Connes' embedding problem and Tsirelson's problem ⋮ Discrete quantum structures. II: Examples ⋮ Graph isomorphism: physical resources, optimization models, and algebraic characterizations ⋮ Spectral bounds for the quantum chromatic number of quantum graphs ⋮ Bisynchronous games and factorizable maps ⋮ Connectivity for quantum graphs ⋮ Positively factorizable maps ⋮ Quantum graphs as quantum relations ⋮ Perfect strategies for non-local games ⋮ Synchronous linear constraint system games

Cites Work

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• Uniqueness of colorability and colorability of planar 4-regular graphs are NP-complete
• Classification of injective factors. Cases \(\mathrm{II}_1\), \(\mathrm{II}_\infty\), \(\mathrm{III}_\lambda\), \(\lambda\neq 1\)
• Synchronous correlation matrices and Connes’ embedding conjecture
• Zero-Error Communication via Quantum Channels, Noncommutative Graphs, and a Quantum Lovász Number
• On the Shannon capacity of a graph

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