A physical approach to Tsirelson's problem

Abstract

Tsirelson's problem deals with how to model separate measurements in quantum mechanics. In addition to its theoretical importance, the resolution of Tsirelson's problem could have great consequences for device independent quantum key distribution and certified randomness. Unfortunately, understanding present literature on the subject requires a heavy mathematical background. In this paper, we introduce quansality, a new theoretical concept that allows to reinterpret Tsirelson's problem from a foundational point of view. Using quansality as a guide, we recover all known results on Tsirelson's problem in a clear and intuitive way.

11 pages, 2 figures

References in corpus (14)

• Device-independent security of quantum cryptography against collective attacks
• Steering, Entanglement, Nonlocality, and the EPR Paradox
• Random Numbers Certified by Bell's Theorem
• A convergent hierarchy of semidefinite programs characterizing the set of quantum correlations
• Bounding the set of quantum correlations
• Secure device-independent quantum key distribution with causally independent measurement devices
• Connes' embedding problem and Tsirelson's problem
• Local Quantum Measurement and No-Signaling Imply Quantum Correlations
• Contractivity of positive and trace preserving maps under $L_p$ norms
• Unified Framework for Correlations in Terms of Local Quantum Observables
• Quantum Cryptography Based Solely on Bell's Theorem
• Device-Independent Quantum Key Distribution with Commuting Measurements
• Tsirelson's Problem
• Sequential Strong Measurements and Heat Vision

Cited by in corpus (14)

• Physical characterization of quantum devices from nonlocal correlations
• Security of device-independent quantum key distribution protocols: a review
• Tsirelson's problem and an embedding theorem for groups arising from non-local games
• Identifying Nonconvexity in the Sets of Limited-Dimension Quantum Correlations
• The Smooth Entropy Formalism for von Neumann Algebras
• An invertible map between Bell non-local and contextuality scenarios
• Quantum Side Information: Uncertainty Relations, Extractors, Channel Simulations
• Quantum Steering and Space-Like Separation
• Secure and robust randomness with sequential quantum measurements
• A bound on the quantum value of all compiled nonlocal games
• Taming identical particles for discerning the genuine non-locality
• Tsirelson's problem and purely atomic von Neumann algebras
• Genuine multipartite entanglement is not necessary for standard device-independent conference key agreement
• Maximally nonlocal subspaces