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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeSep 18th 2023
    • (edited Sep 18th 2023)

    this is a bare sub-section — meant to be !includeed 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”

    v1, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeSep 23rd 2023

    added pointer to what seems to be the original proof:

    Lindblad 1975 (top of p. 149 and inside the proof of Lem. 5).

    diff, v3, current

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeSep 26th 2023

    I have spelled out (here) the proof in one direction (that every endomorphic quantum channel has an evironmental representation)

    diff, v6, current

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeSep 26th 2023
    • (edited Sep 26th 2023)

    More specifically, this usual proof shows that every quantum channel has an environmental representation where the system ρ\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…]