Connections between quantum colorings and quantum automorphism groups

Quantum colorings of graphs arise from winning strategies for a two-player cooperative non-local game, where the players are not allowed to communicate but are allowed to use shared entanglement. Such colorings have very natural descriptions in terms of projection-valued measures in tracial C*-algebras. In this talk, we will look at a recent extension of such colorings to quantum graphs (in the sense of Nik Weaver), focusing on quantum colorings of the so-called "quantum complete graphs". An application of these colorings is that we obtain explicit embeddings of the quantum automorphism group algebras of finite-dimensional C*-algebras (of the same dimension) into matrix algebras over each other. We will see what this means for the strong 1-boundedness of the quantum group von Neumann algebras corresponding to these quantum automorphism groups.