The mathematics of non-local games
William Slofstra, Institute for Quantum Computing
Non-local games are an important subject in quantum information. They provide relatively simple experimental scenarios for testing the axioms of quantum mechanics, and have been proposed for other practical applications, especially in device-independent cryptography. However, we do not know how to answer many of the basic mathematical questions about non-local games. For instance, we do not know how to calculate the optimal winning probability of a non-local game, or what resources might be needed to play a game near-optimally. Due to work of Fritz, Junge et. al., and Ozawa, these questions are closely connected to a long-standing problem in operator algebras, the Connes embedding problem. In this talk, I'll explain how we can get some answers to these basic questions through a connection with combinatorial group theory. I'll also explain why we still have more questions than answers, and what we might hope to do in the future.