  It is shown that local distinguishability of orthogonal mixed states can be
completely characterized by local distinguishability of their supports
irrespective of entanglement and mixedness of the states. This leads to two
kinds of upper bounds on the number of perfect LOCC distinguishable orthogonal
mixed states. The first one depends only on pure-state entanglement within the
supports of the states, and therefore may be easy to compute in many instances.
The second bound is optimal in the sense that it optimizes the bounding
quantities, not necessarily function of entanglement alone, over all orthogonal
mixed state ensembles (satisfying certain conditions) admissible within the
supports of the density matrices.
