Not signed in (Sign In)

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Site Tag Cloud

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor galois-theory gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics planar pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).

nLab > Latest Changes: partial trace

Bottom of Page

1 to 4 of 4

  1.  
    • 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.

1 to 4 of 4

  1.