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Entanglement in Non-local Games and the Hyperlinear Profile of Groups

Slofstra, William and Vidick, Thomas (2018) Entanglement in Non-local Games and the Hyperlinear Profile of Groups. Annales Henri Poincaré, 19 (10). pp. 2979-3005. ISSN 1424-0637. doi:10.1007/s00023-018-0718-y.

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We relate the amount of entanglement required to play linear system non-local games near-optimally to the hyperlinear profile of finitely presented groups. By calculating the hyperlinear profile of a certain group, we give an example of a finite non-local game for which the amount of entanglement required to play ϵ-optimally is at least Ω(1/ϵ^k), f or some k > 0. Since this function approaches infinity as ϵ approaches zero, this provides a quantitative version of a theorem of the first author.

Item Type:Article
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URLURL TypeDescription ReadCube access Paper
Vidick, Thomas0000-0002-6405-365X
Additional Information:© 2018 Springer Nature Switzerland AG. Received: 30 November 2017; Accepted: 10 June 2018; First Online: 02 August 2018. As mentioned in Introduction, we are grateful to Narutaka Ozawa for suggesting the use of the Connes embedding trick and the beautiful line of argument now incorporated in Sect. 5; this led to a substantial improvement in our results. The first author also thanks Martino Lupini for helpful discussions. The second author is supported by NSF CAREER Grant CCF-1553477, AFOSR YIP Award Number FA9550-16-1-0495, a CIFAR Azrieli Global Scholar award, and the IQIM, an NSF Physics Frontiers Center (NSF Grant PHY-1125565) with support of the Gordon and Betty Moore Foundation (GBMF-12500028).
Group:Institute for Quantum Information and Matter
Funding AgencyGrant Number
Air Force Office of Scientific Research (AFOSR)FA9550-16-1-0495
Canadian Institute for Advanced Research (CIFAR)UNSPECIFIED
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
Gordon and Betty Moore FoundationGBMF-12500028
Issue or Number:10
Record Number:CaltechAUTHORS:20180926-132554192
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Official Citation:Slofstra, W. & Vidick, T. Ann. Henri Poincaré (2018) 19: 2979.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:89964
Deposited By: Tony Diaz
Deposited On:26 Sep 2018 21:01
Last Modified:16 Nov 2021 00:39

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