Entanglement, mixedness and perfect local discrimination of orthogonal quantum states

TL;DR

This paper characterizes when orthogonal mixed quantum states can be perfectly distinguished using local operations and classical communication, linking it to their supports and entanglement properties, and provides bounds on distinguishability.

Contribution

It establishes a support-based criterion for local distinguishability of mixed states and derives two bounds related to entanglement and ensemble properties.

Findings

Local distinguishability depends only on the supports of the states.

Two bounds on the number of distinguishable states are derived.

One bound depends solely on pure-state entanglement within supports.

Abstract

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.