IQI Weekly Seminar

Series: Institute for Quantum Information (IQI) Weekly Seminar Series

Information Causality, Szemeredi-Trotter, and algebraic variants of CHSH

Mohammad Bavarian, MIT,

In this work, we consider the following family of two prover one-round
games. In the CHSH_q game, two parties are given x,y in F_q uniformly at random, and each must produce an output a,b in 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 (PRA 2005) as a large alphabet generalization of the celebrated 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. On the way to these results, we also resolve a problem of Pawlowski and Winter about pairwise independent Information Causality, which, beside being interesting on its own, gives as an application a short proof of our upper bound for the entangled value of CHSH_q.

Joint work with Peter W. Shor.

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