2019/05/31 by Alexandru Gheorghiu, Chris Heunen
Physics and Astronomy · Mathematics · #quant-ph #math.CT
paper · pdf · doi:10.4204/eptcs.318.12
published as EPTCS 318, 2020, pp. 196-212 · In Proceedings QPL 2019, arXiv:2004.14750
arxiv created 2020/05/01 · arxiv updated 2020/05/04
We interpret ontological models for finite-dimensional quantum theory as functors from the category of finite-dimensional Hilbert spaces and bounded linear 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 Schrödinger equation. We also prove that it is possible to have epistemic functors that take values in signed Markov kernels.