From Bell Inequalities to Tsirelson's Theorem

David AVIS  Sonoko MORIYAMA  Masaki OWARI  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E92-A   No.5   pp.1254-1267
Publication Date: 2009/05/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E92.A.1254
Print ISSN: 0916-8508
Type of Manuscript: INVITED PAPER (Special Section on Frontier of Quantum Computing)
quantum information,  quantum computation,  quantum correlation,  Bell inequality,  non-local games,  

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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.