Quantum Theory is a Quasi-stochastic Process Theory

Understand

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.