Statistical distinguishability between unitary operations

Details Statistical distinguishability between unitary operations Statistical distinguishability between unitary operations

2001-02-12

arxiv.org/abs/quant-ph/0102064v2

Phys. Rev. Lett 87, 177901 (2001).

Physics

Quantum Physics

6 pages, REVTEX. The perfect distinguishability result is extended to any finite set of gates

Scientific paper

10.1103/PhysRevLett.87.177901

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 $U_1^{\otimes N}$ and $U_2^{\otimes N}$ 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.

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