Ontological models for quantum theory as functors

Alexandru Gheorghiu (California Institute of Technology), Chris Heunen (University og Edinburgh)

We interpret ontological models for quantum theory as functors from the category of C*-algebras and completely positive maps to the category of measurable spaces and Markov kernels. This uniformises several earlier results, that we analyse more closely: Pusey, Barrett, and Rudolph’s result rules out monoidal functors; Leifer and Maroney’s result rules out functors that preserve a duality between states and measurement; Aaronson et al’s result rules out functors that adhere to the Schroedinger equation. We also prove that it is possible to have epistemic functors that take values in signed Markov kernels.