Convex Optimization over Classes of Multiparticle Entanglement

Jiangwei Shang, Otfried Gühne
2018 Physical Review Letters  
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
more » ... pproach, 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)].
doi:10.1103/physrevlett.120.050506 pmid:29481200 fatcat:rfyozaepbvcbrdyzm2jlylx2bu