Information Causality, Szemerédi-Trotter and Algebraic Variants of CHSH

Abstract

In this paper, we consider the following family of two prover one-round games. In the CHSH q game, two parties are given x; y F q uniformly at random, and each must produce an output a; b F q without communicating with the other. The players' objective is to maximize the probability that their outputs satisfy a + b = xy in F q . This game was introduced by Buhrman and Massar [7] as a large alphabet generalization of the CHSH game-which is one of the most well-studied two-prover games in quantum information theory, and which has a large number of applications to quantum cryptography and quantum complexity. Our main contributions in this paper are the first asymptotic and explicit bounds on the entangled and classical values of CHSH q , and the realization of a rather surprising connection between CHSH q and geometric incidence theory.