A synchronous game for binary constraint systems
arXiv:1707.01016 · doi:10.1063/1.4996867
Abstract
Recently, W. Slofstra proved that the set of quantum correlations is not closed. We prove that the set of synchronous quantum correlations is not closed, which implies his result, by giving an example of a synchronous game that has a perfect quantum approximate strategy but no perfect quantum strategy. We also exhibit a graph for which the quantum independence number and the quantum approximate independence number are different. We prove new characterisations of synchronous quantum approximate correlations and synchronous quantum spatial correlations. We solve the synchronous approximation problem of Dykema and the second author, which yields a new equivalence of Connes' embedding problem in terms of synchronous correlations.
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Cited by in corpus (18)
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- Almost synchronous quantum correlations
- Quantum no-signalling correlations and non-local games
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- Noncommutative Nullstellensätze and Perfect Games
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- Relaxations and Exact Solutions to Quantum Max Cut via the Algebraic Structure of Swap Operators
- Geometry of the set of synchronous quantum correlations
- Monogamy of Nonlocal Games
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- The membership problem for constant-sized quantum correlations is undecidable
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