Statistical distinguishability between unitary operations -: art. no. 177901

The problem of distinguishing two unitary transformations, or quantum gates, is analyzed and a function reflecting their statistical distinguishability is found. Given two unitary operations, U-1 and U-2, it is proved that there always exists a finite number N such that U-1(xN) and U-2(xN) are perfectly distinguishable, although they were not in the single-copy case. This result can be extended to any finite set of unitary transformations. Finally, a fidelity for one-qubit gates, which satisfies many useful properties from the point of view of quantum information theory, is presented.