We generalise four well known parameters of graphs to operator systems by considering their underlying quantum channels. In particular, we introduce the Choi-Kraus degree (generalised minimum semidefinite rank) as the dimension of the smallest codomain Hilbert space a quantum channel requires to realise a given operator system as a non-commutative confusability graph.

This is joint work with Vern Paulson, Nick Manor and Ivan Todorov.