Entanglement in non-local games and the hyperlinear profile of groups

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 $\epsilon$-optimally is at least $\Omega (1/{\epsilon }^k)$, for some $k>0$. Since this function approaches infinity as $\epsilon$ approaches zero, this provides a quantitative version of a theorem of the first author.

27 pages. v2: improved results based on a suggestion by N. Ozawa

References in corpus (7)

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• Test for a large amount of entanglement, using few measurements
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Cited by in corpus (8)

• Playing Games with Multiple Access Channels
• Perfect strategies for non-signalling games
• A two-player dimension witness based on embezzlement, and an elementary proof of the non-closure of the set of quantum correlations
• Almost synchronous quantum correlations
• On uniform Hilbert Schmidt stability of groups
• A group with at least subexponential hyperlinear profile
• A three-player coherent state embezzlement game
• Complexity lower bounds for computing the approximately-commuting operator value of non-local games to high precision