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A three-player coherent state embezzlement game

Ji, Zhengfeng and Leung, Debbie and Vidick, Thomas (2020) A three-player coherent state embezzlement game. Quantum, 4 . Art. No. 349. ISSN 2521-327X. doi:10.22331/q-2020-10-26-349.

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We introduce a three-player nonlocal game, with a finite number of classical questions and answers, such that the optimal success probability of 1 in the game can only be achieved in the limit of strategies using arbitrarily high-dimensional entangled states. Precisely, there exists a constant 0 < c ≤ 1 such that to succeed with probability 1 − ε in the game it is necessary to use an entangled state of at leastΩ(ε^(−c)) qubits, and it is sufficient to use a state of at most O(ε⁻¹) qubits. The game is based on the coherent state exchange game of Leung et al. (CJTCS 2013). In our game, the task of the quantum verifier is delegated to a third player by a classical referee. Our results complement those of Slofstra (arXiv:1703.08618) and Dykema et al. (arXiv:1709.05032), who obtained two-player games with similar (though quantitatively weaker) properties based on the representation theory of finitely presented groups and C∗-algebras respectively.

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Vidick, Thomas0000-0002-6405-365X
Additional Information: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. Published: 2020-10-26. We thank William Slofstra and John Watrous for helpful discussions. Part of this work was conducted when ZJ was visiting the Institute for Quantum Computing in the University of Waterloo, and also when DL and TV were attending the “Quantum Physics of Information” program at the Kavli Institute for Theoretical Physics. This research was supported in part by the Australian Research Council under Grant No. DP200100950 and the National Science Foundation under Grant No. NSF PHY 17-48958. DL is supported by an NSERC Discovery grant and a CIFAR research grant via the Quantum Information Science program. TV is supported by NSF CAREER Grant CCF-1553477, AFOSR YIP award number FA9550-16-1-0495, a CIFAR Azrieli Global Scholar award, and the IQIM, an NSF Physics Frontiers Center (NSF Grant PHY-1125565) with support of the Gordon and Betty Moore Foundation (GBMF-12500028).
Group:Institute for Quantum Information and Matter
Funding AgencyGrant Number
Australian Research CouncilDP200100950
NSFPHY 17-48958
Natural Sciences and Engineering Research Council of Canada (NSERC)UNSPECIFIED
Canadian Institute for Advanced Research (CIFAR)UNSPECIFIED
Air Force Office of Scientific Research (AFOSR)FA9550-16-1-0495
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
Gordon and Betty Moore FoundationGBMF-12500028
Record Number:CaltechAUTHORS:20190204-154622144
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:92640
Deposited By: Bonnie Leung
Deposited On:06 Feb 2019 20:30
Last Modified:16 Nov 2021 03:52

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