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Survey on nonlocal games and operator space theory.

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Palazuelos Cabezón, Carlos and Vidick, Thomas (2016) Survey on nonlocal games and operator space theory. Journal of mathematical physics, 57 (1). 015220-1. ISSN 0022-2488

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Official URL: http://scitation.aip.org/content/aip/journal/jmp/57/1/10.1063/1.4938052




Abstract

This review article is concerned with a recently ncovered connection between operator spaces, a noncommutative extension of Banach spaces, and quantum nonlocality, a striking phenomenon which underlies many of the applications of quantum mechanics to information theory, cryptography, and algorithms. Using the framework of nonlocal games, we relate measures of the nonlocality of quantum mechanics to certain norms in the Banach and operator space categories. We survey recent results that exploit this connection to derive large violations of Bell inequalities, study the complexity of the classical and quantum values of games and their relation to Grothendieck inequalities, and quantify the nonlocality of different classes of entangled states.


Item Type:Article
Subjects:Sciences > Mathematics > Mathematical analysis
ID Code:36067
Deposited On:02 Mar 2016 10:05
Last Modified:09 Aug 2016 10:10

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