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I have an arbitrary process matrix that does an entangling operation (a controlled-pi/2 rotation) plus some additional phase rotations that are not of interest. I am curious to find a way to extract a fidelity for how much entanglement a quantum operation creates, so basically ignore the accumulated phase.

Is there a way to directly extract information for how much a quantum operation creates entanglement, i.e. the fidelity with an arbitrary controlled-rotation? So far the best solution I have come up with is to provide some phase rotations to the process matrix and then measure the gate fidelity with a controlled-rotation along x-axis, but I am curious if there are more beautiful solutions.

Thanks a lot!

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