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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 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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