01268nas a2200169   4500000000100000000000100001008004100002100002200043700001500065700001400080700001300094245008900107856004700196300001100243490000700254520083700261       2015                            d1 aZbigniew Puchała1 aA. Jencova1 aM. Sedlak1 aM. Ziman00aExploring boundaries of quantum convex structures: Special role of unitary processes  uhttps://doi.org/10.1103/PhysRevA.92.012304  a0123040 v923 a<p>We address the question of finding the most effective convex decompositions into boundary elements (so-called boundariness) for sets of quantum states, observables and channels. First we show that in general convex sets the boundariness essentially coincides with the question of the most distinguishable element, thus, providing an operational meaning for this concept. Unexpectedly, we discovered that for any interior point of the set of channels the optimal decomposition necessarily contains a unitary channel. In other words, for any given channel the best distinguishable one is some unitary channel. Further, we prove that boundariness is sub-multiplicative under composition of systems and explicitly evaluate its maximal value that is attained only for the most mixed elements of the considered convex structures.</p>