From Bell Inequalities to Tsirelson's Theorem

David AVIS  Sonoko MORIYAMA  Masaki OWARI 

Publication
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
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Frontier of Quantum Computing)
Category: INVITED
Keyword: 
quantum information,  quantum computation,  quantum correlation,  Bell inequality,  non-local games, 

Full Text: PDF(278.2KB)

Summary: 
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.