Non-closure of the set of quantum correlations via graphs

Abstract

We prove that the set of quantum correlations for a bipartite system of 5 inputs and 2 outputs is not closed. Our proof relies on computing the correlation functions of a graph, which is a concept that we introduce.

Version 3: 17 pages. Added an example of a signed game whose synchronous value is not attained. Few typos fixed and minor changes made

References in corpus (4)

• A convergent hierarchy of semidefinite programs characterizing the set of quantum correlations
• Almost quantum correlations
• Connes' embedding problem and Tsirelson's problem
• A synchronous game for binary constraint systems

Cited by in corpus (6)

• Geometry of the set of quantum correlations
• Bigalois extensions and the graph isomorphism game
• Correlation matrices, Clifford algebras, and completely positive semidefinite rank
• Quantum Teleportation and Super-dense Coding in Operator Algebras
• Lower bounds on matrix factorization ranks via noncommutative polynomial optimization
• Bounds on entanglement dimensions and quantum graph parameters via noncommutative polynomial optimization