Distinguishability of states and von Neumann entropy - art. no. 012301

Let {\psi(1)],...,\ psi(n)];p(1),...,p(n)) be an ensemble of pure quantum s tates. We show that it is possible to increase all of the pairwise overlaps \[psi(i)\psi(j)]\, i.e., make each constituent pair of the states more par allel (while keeping the prior probabilities the same), in such a way that the von Neumann entropy S is increased, and dually, make all pairs more ort hogonal while decreasing S. We show that this phenomenon cannot occur for e nsembles in two dimensions but that it is a feature of almost all ensembles of three states in three dimensions. It is known that the von Neumann entr opy characterizes the classical and quantum information capacities of the e nsemble and we argue that information capacity, in rum, is a manifestation of the distinguishability of the signal states. Hence, our result shows tha t the notion of distinguishability within an ensemble is a global property that cannot be reduced to considering distinguishability of each constituen t pair of states.