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