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nLab > Latest Changes: partial trace

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    • CommentRowNumber1.
    • CommentAuthorIan_Durham
    • CommentTimeMar 7th 2010
    Just added a page on partial trace that is presently linked from quantum operations and channels which I also added to. However, note that the partial trace is not specific to physics so it needs embellishing by the mathematicians among us.
    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeMar 8th 2010

    Thanks.

    By the way, there is a simple and natural categorical way to think about this:

    the trace of an endomorphism is defined in any bradied monoidal category with duals (such as Vect): in string diagram notation you simply draw the morphism as a line and then bend that line around and connect its output to its input.

    Now, it that morphism is the endomorphism of a tensor product object V \otimes W , then there is a similarly evident way to "bend around" only the W-strand. That's the partial trace operation.

    This is very simple once one draws the diagram, which I won't do right now.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeMar 8th 2010

    See trace, which should also be interlinked with partial trace

    • CommentRowNumber4.
    • CommentAuthorIan_Durham
    • CommentTimeMar 8th 2010
    Cool! I'll link them up when I get the chance (probably later today). I have to learn how to draw diagrams on nLab, but when I do I can add the diagrams you mentioned.
    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeSep 24th 2023
    • (edited Sep 24th 2023)

    I have tried to fix some of the oddities that this old entry inherited from its original revision 1. (It still leaves much room for improvement.)

    In particular I deleted the lead-in paragraph (which suggested that the partial trace is a concept endemic to quantum physics) and the corresponding example (which looks incorrect to me).

    Instead, I am creating now a separate entry partial trace quantum channel for such discussion.

    diff, v6, current

1 to 5 of 5

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