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nLab > Latest Changes: unistochastic quantum channel

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  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeSep 26th 2023

    recording some reference in reply to the question: “What about quantum channels that admit an environmental representation where the environment starts out in its maximally mixed state?”

    v1, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeSep 26th 2023

    added a couple of paragraphs and some references on the “DQC1” model

    diff, v3, current

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeSep 28th 2023
    • (edited Sep 29th 2023)

    I have spelled out (here) enough of the proof from Müller-Hermes & Perry 2019 (of how mixed unitary QBit channels are unistochastic) to work out the unistochastic presentation (now here) for the example of the spin-flip channel

    [edit: there is something wrong with the last expression. Will check tomorrow.]

    [edit: No, it was correct. But it can of course be simplified further…]

    diff, v7, current

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeSep 29th 2023

    have “simplified” (or made more transparent) the final formula for the uniformly mixed unitary form of the bit-flip channel (now here):

    (It’s an easy computation but I’ve also double-checked with computer algebra.)

    diff, v10, current

1 to 4 of 4

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