Almost synchronous quantum correlations
- URL: http://arxiv.org/abs/2103.02468v3
- Date: Wed, 7 Jun 2023 06:16:50 GMT
- Title: Almost synchronous quantum correlations
- Authors: Thomas Vidick
- Abstract summary: The study of quantum correlation sets was initiated by Tsirelson in the 1980s and originally motivated by questions in the foundations of quantum mechanics.
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.
- Score: 7.716156977428555
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: 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 $\ell_1$ 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.
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