Provable Advantage for Quantum Strategies in Random Symmetric XOR Games

Authors Andris Ambainis, Janis Iraids

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Andris Ambainis
Janis Iraids

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Andris Ambainis and Janis Iraids. Provable Advantage for Quantum Strategies in Random Symmetric XOR Games. In 8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 22, pp. 146-156, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)


Non-local games are widely studied as a model to investigate the properties of quantum mechanics as opposed to classical mechanics. In this paper, we consider a subset of non-local games: symmetric XOR games of n players with 0-1 valued questions. For this class of games, each player receives an input bit and responds with an output bit without communicating to the other players. The winning condition only depends on XOR of output bits and is constant w.r.t. permutation of players. We prove that for almost any n-player symmetric XOR game the entangled value of the game is Theta((sqrt(ln(n)))/(n^{1/4})) adapting an old result by Salem and Zygmund on the asymptotics of random trigonometric polynomials. Consequently, we show that the classical-quantum gap is Theta(sqrt(ln(n))) for almost any symmetric XOR game.
  • Random Symmetric XOR games
  • Entanglement


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