The role of topology in quantum tomography

Abstract

We investigate quantum tomography in scenarios where prior information\nrestricts the state space to a smooth manifold of lower dimensionality. By\nconsidering stability we provide a general framework that relates the topology\nof the manifold to the minimal number of binary measurement settings that is\nnecessary to discriminate any two states on the manifold. We apply these\nfindings to cases where the subset of states under consideration is given by\nstates with bounded rank, fixed spectrum, given unitary symmetry or taken from\na unitary orbit. For all these cases we provide both upper and lower bounds on\nthe minimal number of binary measurement settings necessary to discriminate any\ntwo states of these subsets.\n