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Survey on nonlocal games and operator space theory

Palazuelos, Carlos and Vidick, Thomas (2016) Survey on nonlocal games and operator space theory. Journal of Mathematical Physics, 57 (1). Art. No. 015220. ISSN 0022-2488. doi:10.1063/1.4938052.

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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.

Item Type:Article
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URLURL TypeDescription Paper
Vidick, Thomas0000-0002-6405-365X
Additional Information:© 2016 AIP Publishing LLC. Received 22 September 2015; accepted 2 December 2015; published online 12 January 2016. The first author was supported by Spanish research projects MINECO (Grant No. MTM2011-26912), Comunidad de Madrid (grant QUITEMAD+-CM, Ref. No. S2013/ICE-2801) and Ramón y Cajal program, and the European CHIST-ERA project CQC (funded partially by MINECO Grant No. PRI-PIMCHI-2011-1071). The second author was partially supported by the IQIM, an NSF Physics Frontiers Center (NFS Grant PHY-1125565) with support of the Gordon and Betty Moore Foundation (GBMF-12500028), by the Ministry of Education, Singapore under the Tier 3 grant MOE2012-T3-1-009, and by the Perimeter Institute in Waterloo, Canada.
Group:Institute for Quantum Information and Matter
Funding AgencyGrant Number
Ministerio de Economía y Competitividad (MINECO)MTM2011-26912
Comunidad de MadridQUITEMAD+-CM, Ref. No. S2013/ICE-2801
Ramón y Cajal ProgrammeUNSPECIFIED
European Coordinated Research on Long-term Challenges in Information and Communication Sciences & Technologies ERA-NET (CHIST-ERA)UNSPECIFIED
Ministerio de Economía y Competitividad (MINECO)PRI-PIMCHI-2011-1071
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
NSF Physics Frontiers CenterPHY-1125565
Gordon and Betty Moore FoundationGBMF-12500028
Ministry of Education (Singapore)MOE2012-T3-1-009
Perimeter InstituteUNSPECIFIED
Issue or Number:1
Record Number:CaltechAUTHORS:20160225-142342994
Persistent URL:
Official Citation:Survey on nonlocal games and operator space theory Carlos Palazuelos and Thomas Vidick J. Math. Phys. 57, 015220 (2016);
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:64773
Deposited By: Ruth Sustaita
Deposited On:25 Feb 2016 22:58
Last Modified:10 Nov 2021 23:35

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