Computing and Mathematical Sciences, Caltech
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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 [17]. 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 [26,16,19] involved representation theoretic machinery for finitely-presented groups and $C^*$-algebras.
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Cited by
[1] Ivan Šupić and Joseph Bowles, “Self-testing of quantum systems: a review”, arXiv:1904.10042.
[2] Zhengfeng Ji, Debbie Leung, and Thomas Vidick, “A three-player coherent state embezzlement game”, arXiv:1802.04926.
[3] Zhengfeng Ji, Anand Natarajan, Thomas Vidick, John Wright, and Henry Yuen, “MIP*=RE”, arXiv:2001.04383.
[4] Shubhayan Sarkar, Debashis Saha, Jędrzej Kaniewski, and Remigiusz Augusiak, “Self-testing quantum systems of arbitrary local dimension with minimal number of measurements”, arXiv:1909.12722.
[5] Rui Chao and Ben W. Reichardt, “Quantum dimension test using the uncertainty principle”, arXiv:2002.12432.
[6] Salman Beigi, “Separation of quantum, spatial quantum, and approximate quantum correlations”, arXiv:2004.11103.
The above citations are from SAO/NASA ADS (last updated successfully 2020-06-19 05:53:57). The list may be incomplete as not all publishers provide suitable and complete citation data.
On Crossref’s cited-by service no data on citing works was found (last attempt 2020-06-19 05:53:55).
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Source: https://quantum-journal.org/papers/q-2020-06-18-282/
