eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2013-11-13
146
156
10.4230/LIPIcs.TQC.2013.146
article
Provable Advantage for Quantum Strategies in Random Symmetric XOR Games
Ambainis, Andris
Iraids, Janis
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol022-tqc2013/LIPIcs.TQC.2013.146/LIPIcs.TQC.2013.146.pdf
Random Symmetric XOR games
Entanglement