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