Ontological models for quantum theory as functors

  title={Ontological models for quantum theory as functors},
  author={Alexandru Gheorghiu and Chris Heunen},
  journal={arXiv: Quantum Physics},
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… 

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