Algorithm for characterizing stochastic local operations and classical communication classes of multiparticle entanglement

TL;DR

The paper introduces an algorithmic method to classify multiparticle quantum states based on stochastic local operations and classical communication, aiding in understanding their entanglement properties.

Contribution

It generalizes a recent separability algorithm to classify states within convex sets related to entanglement classes.

Findings

Algorithm effectively determines if a state belongs to a specific convex set.

Applicable to various examples demonstrating broad utility.

Provides a way to find a neighborhood around a state within the same convex set.

Abstract

It is well known that the classification of pure multiparticle entangled states according to stochastic local operations leads to a natural classification of mixed states in terms of convex sets. We present a simple algorithmic procedure to prove that a quantum state lies within a given convex set. Our algorithm generalizes a recent algorithm for proving separability of quantum states [J. Barreiro et al., Nature Phys. 6, 943 (2010)]. We give several examples which show the wide applicability of our approach. We also propose a procedure to determine a vicinity of a given quantum state which still belongs to the considered convex set.