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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.
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