Quantum XOR games

Oded Regev, Thomas Vidick

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Article number15
JournalACM Transactions on Computation Theory
Volume7
Issue number4
DOIs
StatePublished - Aug 1 2015

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Quantum Games
Entanglement
Game
Byproducts
Entangled State
Quantum State
Sharing
Efficient Algorithms
Arbitrary
Approximation
Model
Range of data

Keywords

  • Entangled games
  • F.1.2. [modes of computation]: quantum computing
  • Grothendieck inequality
  • Theory
  • XOR games

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Theoretical Computer Science

Cite this

Quantum XOR games. / Regev, Oded; Vidick, Thomas.

In: ACM Transactions on Computation Theory, Vol. 7, No. 4, 15, 01.08.2015.

Research output: Contribution to journalArticle

Regev, Oded ; Vidick, Thomas. / Quantum XOR games. In: ACM Transactions on Computation Theory. 2015 ; Vol. 7, No. 4.
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