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

Andrea Coladangelo

doi:10.22331/q-2020-06-18-282

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

Andrea Coladangelo

Computing and Mathematical Sciences, Caltech

Published:	2020-06-18, volume 4, page 282
Eprint:	arXiv:1904.02350v3
Doi:	https://doi.org/10.22331/q-2020-06-18-282
Citation:	Quantum 4, 282 (2020).

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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.

► BibTeX data

@article{Coladangelo2020twoplayerdimension,
  doi = {10.22331/q-2020-06-18-282},
  url = {https://doi.org/10.22331/q-2020-06-18-282},
  title = {A two-player dimension witness based on embezzlement, and an elementary proof of the non-closure of the set of quantum correlations},
  author = {Coladangelo, Andrea},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {4},
  pages = {282},
  month = jun,
  year = {2020}
}

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Cited by

[1] Ivan Šupić and Joseph Bowles, "Self-testing of quantum systems: a review", Quantum 4, 337 (2020).

[2] Ivan Šupić, "Nonlocality strikes again", Quantum Views 4, 38 (2020).

[3] Andrea Coladangelo and Jalex Stark, "An inherently infinite-dimensional quantum correlation", Nature Communications 11 1, 3335 (2020).

[4] Matthias Christandl, Nicholas Gauguin Houghton-Larsen, and Laura Mancinska, "An Operational Environment for Quantum Self-Testing", Quantum 6, 699 (2022).

[5] Shubhayan Sarkar, "An Operational Notion of Classicality Based on Physical Principles", Foundations of Physics 53 2, 47 (2023).

[6] Zhengfeng Ji, Debbie Leung, and Thomas Vidick, "A three-player coherent state embezzlement game", Quantum 4, 349 (2020).

[7] Salman Beigi, "Separation of quantum, spatial quantum, and approximate quantum correlations", Quantum 5, 389 (2021).

[8] Shubhayan Sarkar, Debashis Saha, Jędrzej Kaniewski, and Remigiusz Augusiak, "Self-testing quantum systems of arbitrary local dimension with minimal number of measurements", npj Quantum Information 7 1, 151 (2021).

[9] Zhengfeng Ji, Anand Natarajan, Thomas Vidick, John Wright, and Henry Yuen, "MIP*=RE", arXiv:2001.04383, (2020).

[10] Ranyiliu Chen, Jurij Volčič, and Laura Mančinska, "All Projective Measurements Can be Self-tested", arXiv:2302.00974, (2023).

[11] Rui Chao and Ben W. Reichardt, "Quantum dimension test using the uncertainty principle", arXiv:2002.12432, (2020).

The above citations are from Crossref's cited-by service (last updated successfully 2023-05-29 21:33:18) and SAO/NASA ADS (last updated successfully 2023-05-29 21:33:19). The list may be incomplete as not all publishers provide suitable and complete citation data.

This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.

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

Abstract

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