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Almost synchronous quantum correlations

Vidick, Thomas (2022) Almost synchronous quantum correlations. Journal of Mathematical Physics, 63 (2). Art. No. 022201. ISSN 0022-2488. doi:10.1063/5.0056512.

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The study of quantum correlation sets initiated by Tsirelson in the 1980s and originally motivated by questions in the foundations of quantum mechanics has more recently been tied to questions in quantum cryptography, complexity theory, operator space theory, group theory, and more. Synchronous correlation sets introduced by Paulsen et al. [J. Funct. Anal. 270, 2188–2222 (2016)] are a subclass of correlations that has proven particularly useful to study and arises naturally in applications. We show that any correlation that is almost synchronous, in a natural ℓ1 sense, arises from a state and measurement operators that are well-approximated by a convex combination of projective measurements on a maximally entangled state. This extends a result of Paulsen et al. [J. Funct. Anal. 270, 2188–2222 (2016)] that applies to exactly synchronous correlations. Crucially, the quality of approximation is independent of the dimension of the Hilbert spaces or of the size of the correlation. Our result allows one to reduce the analysis of many classes of nonlocal games, including rigidity properties, to the case of strategies using maximally entangled states that are generally easier to manipulate.

Item Type:Article
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URLURL TypeDescription Paper
Vidick, Thomas0000-0002-6405-365X
Additional Information:© 2022. Published under an exclusive license by AIP Publishing. Submitted: 11 May 2021; Accepted: 10 January 2022; Published Online: 2 February 2022. I thank Laura Mančinska, William Slofstra, and Henry Yuen for comments and Vern Paulsen for pointing out typos in an earlier version. This work was supported by NSF CAREER Grant No. CCF-1553477, AFOSR YIP Award No. FA9550-16-1-0495, MURI Grant No. FA9550-18-1-0161, and the IQIM, an NSF Physics Frontiers Center (NSF Grant No. PHY-1125565) with support of the Gordon and Betty Moore Foundation (Grant No. GBMF-12500028). The author has no conflicts of interest to disclose. Data Availability: Data sharing is not applicable to this article as no new data were created or analyzed in this study.
Group:Institute for Quantum Information and Matter
Funding AgencyGrant Number
Air Force Office of Scientific Research (AFOSR)FA9550-16-1-0495
Air Force Office of Scientific Research (AFOSR)FA9550-18-1-0161
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
Gordon and Betty Moore FoundationGBMF-12500028
Issue or Number:2
Record Number:CaltechAUTHORS:20211006-163212999
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Official Citation:Thomas Vidick , "Almost synchronous quantum correlations", J. Math. Phys. 63, 022201 (2022)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:111240
Deposited By: Tony Diaz
Deposited On:06 Oct 2021 16:42
Last Modified:02 Feb 2022 19:02

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