Diagnostics of quantum-gate coherences deteriorated by unitary errors via end-point-measurement statistics

Quantum coherence is a central ingredient in quantum physics with several theoretical and technological ramifications. We consider a figure of merit encoding the information on how the coherence generated on average by a quantum gate is affected by unitary errors (coherent noise sources) in the form of rotation-angle and rotation-axis errors. We provide numerical evidences that such information is well captured by the statistics of local energy measurements on the output states of the gate. These findings are then corroborated by experimental data taken in a quantum optics setting.