Probabilistic Operator Algebra Seminar: Non-closure of a set of quantum correlations

Seminar | April 16 | 2-4 p.m. | 736 Evans Hall

 Ken Dykema, Texas A&M University

 Department of Mathematics

Several different models exist for quantum strategies for non-local games (e.g. the graph coloring game ). Different sets correspond to different sets of correlation matrices. Open questions about these sets of correlation matrices remain, including some that are equivalent to Connes' Embedding Conjecture. One set of correlation matrices is the set arising from finite dimensional projections. The question of whether this set is always closed was solved by William Slofstra in early 2017.

In this talk we will briefly introduce the theory of quantum strategies for non-local games and the corresponding set of correlation matrices, and we will describe the current state of knowledge about them. Then we will discuss a newer proof of Slofstra's result, which actually works for games with fewer inputs and outputs than Slofstra required. The latter result is joint work with Vern Paulsen and Jitendra Prakash.