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I have a target unitary that I want to implement and I have a known dynamics that results in a quantum channel. I already have some fidelity measures to characterize the overlap between them. (like: https://arxiv.org/abs/0909.0077) But I want a more straightforward method to see their difference.

What I have in mind is something like separating the quantum channel into two parts. One is the 'unitary' part that only involves rotation of the state vector. The other is decoherence which causes the Bloch vector to 'shrink'. It sounds like finding two sets of Kraus operators. Is there a way to do this and compare the 'unitary' part of the quantum channel with the target unitary?

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  • $\begingroup$ you mean like using the Stinespring dilation? That way you describe the channel as a unitary dynamics in an enlarged space, and decoherence and other non-unitary effects come from partial tracing the ancillary degrees of freedom $\endgroup$
    – glS ♦
    Jan 26 at 12:46
  • $\begingroup$ @glS Thanks for your reply! However, I'm trying to compare the channel with a unitary on the same space. In fact, I'm trying to find some fidelity measures for gate realization. The paper attached is a good one but I want something with better detail. $\endgroup$
    – Will Yang
    Jan 26 at 23:36

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I found the following two works solving this problem. They selected several reference states and took the HS product between the final states evolved by the target unitary and the quantum channel. https://journals.aps.org/pra/abstract/10.1103/PhysRevA.88.042309 https://iopscience.iop.org/article/10.1088/1367-2630/16/5/055012

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  • $\begingroup$ I'm not sure if this is what you're looking for, but given that it seems like you're essentially trying to compare two different channels (one of which is a unitary channel), section 3.3 of Watrous' book might also be of interest: cs.uwaterloo.ca/~watrous/TQI. $\endgroup$
    – glS ♦
    Apr 26 at 9:36

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