This review article is concerned with a recently uncovered 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.
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January 2016
Research Article|
January 12 2016
Survey on nonlocal games and operator space theory
Carlos Palazuelos;
Carlos Palazuelos
a)
1Instituto de Ciencias Matemáticas (ICMAT), Facultad de Ciencias Matemáticas,
Universidad Complutense de Madrid
, Madrid, Spain
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Thomas Vidick
Thomas Vidick
b)
2Department of Computing and Mathematical Sciences,
California Institute of Technology
, Pasadena, California 91125, USA
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a)
Email: cpalazue@mat.ucm.es
b)
Email: vidick@cms.caltech.edu
J. Math. Phys. 57, 015220 (2016)
Article history
Received:
September 22 2015
Accepted:
December 02 2015
Citation
Carlos Palazuelos, Thomas Vidick; Survey on nonlocal games and operator space theory. J. Math. Phys. 1 January 2016; 57 (1): 015220. https://doi.org/10.1063/1.4938052
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