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arXiv · 1904.02350

A two-player dimension witness based on embezzlement, and an elementary proof of the non-closure of the set of quantum correlations

Andrea Coladangelo
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Abstract

We describe a two-player non-local game, with a fixed small number of questions and answers, such that an $\epsilon$-close to optimal strategy requires an entangled state of dimension $2^{\Omega(\epsilon^{-1/8})}$. Our non-local game is inspired by the three-player non-local game of Ji, Leung and Vidick [arXiv:1802.04926]. It reduces the number of players from three to two, as well as the question and answer set sizes. Moreover, it provides an (arguably) elementary proof of the non-closure of the set of quantum correlations, based on embezzlement and self-testing. In contrast, previous proofs involved representation theoretic machinery for finitely-presented groups and $C^*$-algebras.

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Andrea Coladangelo. 2019-04-04. A two-player dimension witness based on embezzlement, and an elementary proof of the non-closure of the set of quantum correlations. https://doi.org/10.22331/q-2020-06-18-282

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