Separable Operations on Pure States

TL;DR

This paper characterizes the ensembles resulting from separable operations on pure bipartite states using majorization conditions, extending known LOCC results to all separable operations.

Contribution

It provides a complete characterization of separable operations on pure states via majorization, unifying and extending LOCC results.

Findings

Separable operations are characterized by a majorization condition.

Results for LOCC are applicable to all separable operations.

Monotonicity of entanglement extends to separable operations.

Abstract

We show that the possible ensembles produced when a separable operation acts on a single pure bipartite entangled state are completely characterized by a majorization condition, a collection of inequalities for Schmidt coefficients, which is identical to that already known for the particular case of local operations and classical communication (LOCC). As a consequence, various known results for LOCC, including some involving monotonicity of entanglement, can be extended to the class of all separable operations.