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Distinguishing classically indistinguishable states and channels

Research paper by Kamil Korzekwa, Stanisław Czachórski, Zbigniew Puchała, Karol Życzkowski

Indexed on: 21 Dec '18Published on: 21 Dec '18Published in: arXiv - Quantum Physics



Abstract

We investigate an original family of quantum distinguishability problems, where the goal is to perfectly distinguish between $M$ quantum states that become identical under a completely decohering map. Similarly, we study distinguishability of $M$ quantum channels that cannot be distinguished when one is restricted to decohered input and output states. The studied problems arise naturally in the presence of a superselection rule, allow one to quantify the amount of information that can be encoded in phase degrees of freedom (coherences), and are related to time-energy uncertainty relation. We present a collection of results on both necessary and sufficient conditions for the existence of $M$ perfectly distinguishable states (channels) that are classically indistinguishable.