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.
BT - Phys. Rev. A DO - 10.1103/PhysRevA.92.012304 LA - eng N2 -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.
PY - 2015 EP - 012304 T2 - Phys. Rev. A TI - Exploring boundaries of quantum convex structures: Special role of unitary processes UR - https://doi.org/10.1103/PhysRevA.92.012304 VL - 92 ER -