Quantum Theory is a Quasi-stochastic Process Theory

@article{Wetering2017QuantumTI,
  title={Quantum Theory is a Quasi-stochastic Process Theory},
  author={John van de Wetering},
  journal={arXiv: Quantum Physics},
  year={2017}
}
There is a long history of representing a quantum state using a quasi-probability distribution: a distribution allowing negative values. In this paper we extend such representations to deal with quantum channels. The result is a convex, strongly monoidal, functorial embedding of the category of trace preserving completely positive maps into the category of quasi-stochastic matrices. This establishes quantum theory as a subcategory of quasi-stochastic processes. Such an embedding is induced by a… 
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