01353nas a2200169   4500000000100000000000100001008004100002100001900043700002700062700002200089700002200111245006900133856003700202300001100239490000700250520092600257       2019                            d1 aKamil Korzekwa1 aStanisław Czachórski1 aZbigniew Puchała1 aKarol Życzkowski00aDistinguishing classically indistinguishable states and channels  uhttps://arxiv.org/abs/1812.09083  a4753030 v523 a<p>We investigate an original family of quantum distinguishability problems, where the goal is to perfectly distinguish between <span style="font-size:129%"><em>M</em></span> quantum states that become identical under a completely decohering map. Similarly, we study distinguishability of <span style="font-size:129%"><em>M</em></span> 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 <span style="font-size:129%"><em>M</em></span> perfectly distinguishable states (channels) that are classically indistinguishable.</p>