Jop Briët: Unbounded violations of three-player XOR games: Improved, simplified and explicit constructions

Monday, May 14, 2012 12:30 pm - 1:30 pm EDT (GMT -04:00)

Jop Briët, Centrum Wiskunde & Informatica (CWI)

Abstract

XOR games are the simplest model in which the nonlocal properties of entanglement manifest themselves. When there are two players, it is well known that the bias — the maximum advantage over random play — of entangled players can be at most a constant times greater than that of classical players. Recently, Perez-Garcia et al. (2008) showed that no such bound holds when there are three or more players. Their proof relies on non-trivial results from operator-space theory, and gives a non-explicit existence proof, leading to a game with a very large number of questions and only a loose control over the local dimension of the players’ shared entanglement. In this talk, I will explain an improved, simple and explicit (though still probabilistic) construction of a family of three-player XOR games which achieve a large violation.

Joint work with Thomas Vidick.