Operational Representations in Categorical Quantum Mechanics

Abramsky and Heunen have recently established the connection between operational theories and categorical quantum mechanics which are two useful formalisms to understand the unique properties of quantum mechanics and to provide different perspective on the results in quantum foundations and quantum information. From this point of view, monoidal dagger categories equipped with a trace ideal give rise to operational representation which is derived from a formulation of compound systems in an operational theory. One can also formulate non-locality within this framework. The aim of this project is to extend the current approach of non-locality to a sheaf-theoretic setting. We also intend to study the examples from this new perpective, such as the category of sets and relations Rel and the category Spek which is the category for Spekkens' toy theory.