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The presence of an additive conserved quantity imposes a limitation on themeasurement process. According to the Wigner-Araki-Yanase theorem, the perfectrepeatability and the distinguishability on the apparatus cannot be attainedsimultaneously. Instead of the repeatability, in this paper, thedistinguishability on both systems is examined. We derive a trade-offinequality between the distinguishability of the final states on the system andthe one on the apparatus. The inequality shows that the perfectdistinguishability of both systems cannot be attained simultaneously.Comment: To be published in Phys.Rev.

Wigner-Araki-Yanase theorem on distinguishability