Separation of quantum, spatial quantum, and approximate quantum correlations

Abstract

Quantum nonlocal correlations are generated by implementation of local quantum measurements on spatially separated quantum subsystems. Depending on the underlying mathematical model, various notions of sets of quantum correlations can be defined. In this paper we prove separations of such sets of quantum correlations. In particular, we show that the set of bipartite quantum correlations with four binary measurements per party becomes strictly smaller once we restrict the local Hilbert spaces to be finite dimensional, i.e., ${\mathcal{C}}_q^{(4,4,2,2)}\ne {\mathcal{C}}_{qs}^{(4,4,2,2)}$. We also prove non-closure of the set of bipartite quantum correlations with four ternary measurements per party, i.e., ${\mathcal{C}}_{qs}^{(4,4,3,3)}\ne {\mathcal{C}}_{qa}^{(4,4,3,3)}$.

arXiv comment25 pages, 3 tables

References in corpus (17)

• Randomness vs Non Locality and Entanglement
• All Pure Bipartite Entangled States can be Self-Tested
• Sum-of-squares decompositions for a family of CHSH-like inequalities and their application to self-testing
• Maximal violation of the I3322 inequality using infinite dimensional quantum systems
• Embezzling Entangled Quantum States
• Tsirelson's problem and Kirchberg's conjecture
• Robust Self Testing of Unknown Quantum Systems into Any Entangled Two-Qubit States
• Bell inequalities tailored to maximally entangled states
• Tsirelson's problem and an embedding theorem for groups arising from non-local games
• Tsirelson's Problem
• Unconditional separation of finite and infinite-dimensional quantum correlations
• Coherent state exchange in multi-prover quantum interactive proof systems
• MIP*=RE
• A generalization of the CHSH inequality self-testing maximally entangled states of any local dimension
• Non-closure of quantum correlation matrices and factorizable channels that require infinite dimensional ancilla
• A two-player dimension witness based on embezzlement, and an elementary proof of the non-closure of the set of quantum correlations
• Self-testing quantum systems of arbitrary local dimension with minimal number of measurements

Cited by in corpus (4)

• Semidefinite programming relaxations for quantum correlations
• Self-testing of multipartite GHZ states of arbitrary local dimension with arbitrary number of measurements per party
• A bound on the quantum value of all compiled nonlocal games
• An operator-algebraic formulation of self-testing