1
$\begingroup$

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?

$\endgroup$
7
  • $\begingroup$ 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

0

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Browse other questions tagged or ask your own question.