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I am working on a project and I expect to have expressions of a bunch of quantum channels of interest. The quantum channels will be in matrix form. For example for a 2 qubit system, the quantum channel will be given by a 16 by 16 matrix.

Is there any systematic way to use the matrix representations of quantum channels and find the corresponding Kraus operators etc? Find which channels correspond to unitary channels etc?

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  • $\begingroup$ This might be helpful: quantumcomputing.stackexchange.com/a/5816/13968 $\endgroup$
    – narip
    Nov 21, 2022 at 2:10
  • $\begingroup$ There are multiple representations of channels using a single, necessarily square matrix, most notably the Choi and $\chi$ matrix. See e.g. this previous answer of mine. For both these we have: 1) the eigenvectors correspond to the Kraus operators and 2) if the matrix is single rank it corresponds to a unitary. If you let us know what representation you will work with I can write up a more detailed answer. $\endgroup$
    – JSdJ
    Nov 21, 2022 at 8:28
  • $\begingroup$ you can also find a bunch of explicit examples of matrix representations (with a focus on Chois and Stinespring isometries) in quantumcomputing.stackexchange.com/q/24511/55. Does any of these linked posts answer your question? If not, could you further clarify what you are asking and how it differs from the other related discussions? $\endgroup$
    – glS ♦
    Nov 21, 2022 at 9:32
  • $\begingroup$ I have yet to perform the computation but I expect to have a bunch of matrices in the usual sense. I'll have to throw away the matrices that don't correspond to CPTP maps. I'll then like to identify the remaining matrices/CPTP maps with their Kraus and/or Choi decomposition. $\endgroup$
    – user22511
    Nov 21, 2022 at 16:12
  • $\begingroup$ @user22511 that still doesn't clarify the problem. There are multiple possible matrix representations of a channel. You need to specify which one you are talking about. $\endgroup$
    – glS ♦
    Nov 21, 2022 at 18:13

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