Convex optimization over classes of multiparticle entanglement

TL;DR

This paper introduces two convex optimization algorithms tailored for classifying multiparticle entanglement within SLOCC classes, demonstrating their effectiveness on experimental data involving bound entanglement.

Contribution

It adapts Gilbert's algorithm for entanglement classification and develops two new convex optimization methods for analyzing multiparticle entanglement classes.

Findings

Algorithms successfully classify multiparticle entanglement.

Application to experimental data confirms effectiveness.

Enhanced tools for entanglement analysis in quantum information.

Abstract

A well-known strategy to characterize multiparticle entanglement utilizes the notion of stochastic local operations and classical communication (SLOCC), but characterizing the resulting entanglement classes is difficult. Given a multiparticle quantum state, we first show that Gilbert's algorithm can be adapted to prove separability or membership in a certain entanglement class. We then present two algorithms for convex optimization over SLOCC classes. The first algorithm uses a simple gradient approach, while the other one employs the accelerated projected-gradient method. For demonstration, the algorithms are applied to the likelihood-ratio test using experimental data on bound entanglement of a noisy four-photon Smolin state [Phys. Rev. Lett. 105, 130501 (2010)].