From Bell Inequalities to Tsirelson's Theorem: A Survey

Abstract

The first part of this paper contains an introduction to Bell inequalities and Tsirelson's theorem for the non-specialist. The next part gives an explicit optimum construction for the "hard" part of Tsirelson's theorem. In the final part we describe how upper bounds on the maximal quantum violation of Bell inequalities can be obtained by an extension of Tsirelson's theorem, and survey very recent results on how exact bounds may be obtained by solving an infinite series of semidefinite programs.

25 pages

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• Graphical description of the action of local Clifford transformations on graph states
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Cited by in corpus (9)

• Bell nonlocality
• Characterizing finite-dimensional quantum behavior
• Improved local models and new Bell inequalities via Frank-Wolfe algorithms
• Belief-Invariant and Quantum Equilibria in Games of Incomplete Information
• A method for systematic construction of Bell-like inequalities and a proposal of a new type of test
• Correlation matrices, Clifford algebras, and completely positive semidefinite rank
• A Close Look at the EPR Data of Weihs et al
• Characterization of non-signaling correlations from mutual information
• Bounds on Multipartite Nonlocality via Reduction to Biased Nonlocality