Transformations of $W$-Type Entangled States

TL;DR

This paper investigates how $W$-type entangled states can be transformed using local operations and classical communication, providing a complete characterization and conditions for deterministic transformations, along with bounds on distillation probabilities.

Contribution

It introduces a new parametrization of $W$-states invariant under local unitaries and derives necessary and sufficient conditions for their deterministic transformation.

Findings

Complete characterization of local operations for $W$-states

Necessary and sufficient conditions for deterministic transformations

Upper bounds on distillation probabilities

Abstract

The transformations of $W$-type entangled states by using local operations assisted with classical communication are investigated. For this purpose, a parametrization of the $W$-type states which remains invariant under local unitary transformations is proposed and a complete characterization of the local operations carried out by a single party is given. These are used for deriving the necessary and sufficient conditions for deterministic transformations. A convenient upper bound for the maximum probability of distillation of arbitrary target states is also found.