  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.
