Quantum symmetries of quantum metric spaces

A light introduction to the theory of compact quantum groups. We look at quantum metric spaces, a non-commutative analogue of finite metric spaces. Banica has defined the quantum symmetry group of a finite metric space, and this talk shows how to capture Banica’s definition using the Weaver–Kuperberg framework of quantum metric spaces, connecting the extension to the theory of non-local games.

Further reading: Eifler, “Non-local games and quantum symmetries of quantum metric spaces” (arXiv:2011.03867).