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Almost synchronous quantum correlations

Vidick, Thomas (2021) Almost synchronous quantum correlations. . (Unpublished)

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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 in [Paulsen et. al, JFA 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, JFA 2016] which 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 which are generally easier to manipulate.

Item Type:Report or Paper (Discussion Paper)
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URLURL TypeDescription Paper
Vidick, Thomas0000-0002-6405-365X
Additional Information:Attribution 4.0 International (CC BY 4.0). I thank Laura Mančinska, William Slofstra and Henry Yuen for comments and Vern Paulsen for pointing out typos in an earlier version. This work is supported by NSF CAREER Grant CCF-1553477, AFOSR YIP award number FA9550-16-1-0495, MURI Grant FA9550-18-1-0161 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
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
Record Number:CaltechAUTHORS:20211006-163212999
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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:06 Oct 2021 16:42

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