Constructions of genuinely entangled multipartite states with applications to local hidden variables (LHV) and states (LHS) models

TL;DR

This paper presents a general method for constructing genuinely entangled multipartite quantum states from smaller entangled states, with applications to local hidden variables and models, and introduces criteria to verify genuine entanglement efficiently.

Contribution

It develops a novel approach to generate multipartite entangled states from bipartite states using isometries, and provides criteria for verifying genuine entanglement.

Findings

Constructed multipartite states that are genuinely entangled but not genuinely nonlocal.

Demonstrated the creation of genuinely entangled states that are unsteerable across certain cuts.

Provided efficient criteria for verifying genuine entanglement in complex states.

Abstract

Building upon the results of [R. Augusiak et al., Phys. Rev. Lett. 115, 030404 (2015)] we develop a general approach to the generation of genuinely entangled multipartite states of any number of parties from genuinely entangled states of a fixed number of parties, in particular, the bipartite entangled ones. In our approach, certain isometries whose output subspaces are either symmetric or genuinely entangled in some multipartite Hilbert spaces are applied to local subsystems of bipartite entangled or multipartite genuinely entangled quantum states. To prove that entanglement of the resulting states is indeed genuine we then introduce novel criteria allowing to decide it efficiently. The construction is then exploited to provide examples of multipartite states that are genuinely entangled but not genuinely nonlocal, giving further illustration for the inequivalence between entanglement and nonlocality in the multiparticle scenario. It is also shown how to construct genuinely entangled states which are unsteerable across certain bipartite cuts.