Speaker: Samuel Harris, University of Waterloo

Connes' embedding problem and quantum XOR games

One of the most significant outstanding problems in operator algebras is Connes' embedding problem. In recent years, a deep connection has been exhibited between this problem and the weak Tsirelson problem regarding quantum bipartite probabilities.  Motivated by this connection, we will briefly outline the theory of two-player quantum XOR games, and how unitary correlations can be thought of as strategies for these games.

These correlations naturally arise from states on various tensor products of certain universal operator systems.  We will show that the embedding problem holds if and only if every quantum XOR game with a winning strategy in the quantum commuting model also has a winning strategy in the approximate finite-dimensional (quantum approximate) model. In other words, the class of quantum XOR games is a rich enough class of (generalized) non-local games to detect the validity of the embedding problem.