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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. http://resolver.caltech.edu/CaltechAUTHORS:20180926-132554192

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Abstract

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
Related URLs:
URLURL TypeDescription
https://doi.org/10.1007/s00023-018-0718-yDOIArticle
https://rdcu.be/7PMkPublisherFree ReadCube access
https://arxiv.org/abs/1711.10676arXivDiscussion Paper
ORCID:
AuthorORCID
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:IQIM, Institute for Quantum Information and Matter
Funders:
Funding AgencyGrant Number
NSFCCF-1553477
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
NSFPHY-1125565
Gordon and Betty Moore FoundationGBMF-12500028
Record Number:CaltechAUTHORS:20180926-132554192
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20180926-132554192
Official Citation:Slofstra, W. & Vidick, T. Ann. Henri Poincaré (2018) 19: 2979. https://doi.org/10.1007/s00023-018-0718-y
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:89964
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:26 Sep 2018 21:01
Last Modified:26 Sep 2018 21:01

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