Construction of genuinely entangled multipartite subspaces from bipartite ones by reducing the total number of separated parties

TL;DR

This paper presents a method to construct genuinely entangled multipartite subspaces from bipartite entangled subspaces, aiding in entanglement detection and the creation of distillable subspaces across all bipartite cuts.

Contribution

It introduces a novel approach to generate genuinely entangled multipartite subspaces from bipartite ones and explores their applications in entanglement detection and distillability.

Findings

Genuinely entangled subspaces can be constructed from bipartite entangled subspaces.

Direct sums of these subspaces can also be genuinely entangled.

The method aids in detecting entanglement in tensor product states and constructing distillable subspaces.

Abstract

Construction of genuinely entangled multipartite subspaces with certain characteristics has become a relevant task in various branches of quantum information. Here we show that such subspaces can be obtained from an arbitrary collection of bipartite entangled subspaces under joining of their adjacent subsystems. In addition, it is shown that direct sums of such constructions under certain conditions are genuinely entangled. These facts are then used in detecting entanglement of tensor products of mixed states and constructing subspaces that are distillable across every bipartite cut, where for the former application we include example with the analysis of genuine entanglement of a tripartite state obtained from two Werner states.