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this is a bare sub-section — meant to be !include
ed into relevant entries such as at quantum channel and at quantum decoherence — towards the theorem that quantum channels are exactly the “bath-averages of bath-coupled unitary evolutions”
added pointer to what seems to be the original proof:
Lindblad 1975 (top of p. 149 and inside the proof of Lem. 5).
More specifically, this usual proof shows that every quantum channel has an environmental representation where the system $\rho$ gets coupled to a pure state of the environment.
Question: Which quantum channels have an environmental representation where the systems gets coupled to the uniform (identity matrix-)state of the environment? Is this known?
[edit: Oh, never mind. I see now this works by using “canonical Kraus form”. Will edit…]
[edit: Ah, it does not work generally, but for unistochastic channels…]
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