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I am aware that the rank of the Choi state is a test for whether or not a channel is unitary.

Are there any other equivalent tests that we can do to test if a channel is unitary without involving a reference register? I am assuming I have the channel available to me as a black box and can send arbitrary inputs and measure the outputs (even tomography on the outputs).

Frederik vom Ende
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asdfghj
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1 Answers1

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A naive approach is to perform quantum process tomography and characterize the process matrix $\chi$. However, there is a body of work on learning quantum dynamics, some of which explicitly focuses on learning the unitarity, which is a measure of how unitary the channel is. Here are a couple of possibly helpful papers.

[1] https://arxiv.org/abs/1503.07865

[2] https://arxiv.org/abs/2212.09319

Rohan Mehta
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