The talk will be a survey of recent work on the connections between

group operator systems and non-signalling correlations. I will show how tensor products in the operator system category can be interpreted as physical theories, and will exhibit a refinement of non-signalling corrections giving rise to quantum attributes of graphs, including quantum versions of the chromatic and the fractional chromatic number. Relations between the parameters will be examined and further directions will be discussed.

Coauthors: V. I. Paulsen, S. Severini, D. Stahlke, A. Winter