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Quantum XOR Games

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Published:31 August 2015Publication History
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Abstract

We introduce quantum XOR games, a model of two-player, one-round games that extends the model of XOR games by allowing the referee’s questions to the players to be quantum states. We give examples showing that quantum XOR games exhibit a wide range of behaviors that are known not to exist for standard XOR games, such as cases in which the use of entanglement leads to an arbitrarily large advantage over the use of no entanglement. By invoking two deep extensions of Grothendieck’s inequality, we present an efficient algorithm that gives a constant-factor approximation to the best performance that players can obtain in a given game, both in the case that they have no shared entanglement and that they share unlimited entanglement. As a byproduct of the algorithm, we prove some additional interesting properties of quantum XOR games, such as the fact that sharing a maximally entangled state of arbitrary dimension gives only a small advantage over having no entanglement at all.

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    • Published in

      cover image ACM Transactions on Computation Theory
      ACM Transactions on Computation Theory  Volume 7, Issue 4
      September 2015
      110 pages
      ISSN:1942-3454
      EISSN:1942-3462
      DOI:10.1145/2818749
      Issue’s Table of Contents

      Copyright © 2015 ACM

      Publisher

      Association for Computing Machinery

      New York, NY, United States

      Publication History

      • Published: 31 August 2015
      • Revised: 1 May 2015
      • Accepted: 1 May 2015
      • Received: 1 February 2013
      Published in toct Volume 7, Issue 4

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