Ontological models for quantum theory as functors

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

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.

In Bob Coecke and Matthew Leifer: Proceedings 16th International Conference on Quantum Physics and Logic (QPL 2019), Chapman University, Orange, CA, USA., 10-14 June 2019, Electronic Proceedings in Theoretical Computer Science 318, pp. 196–212.
Published: 1st May 2020.

ArXived at: http://dx.doi.org/10.4204/EPTCS.318.12 bibtex PDF
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