Tripartite genuinely entangled states from entanglement-breaking subspaces

TL;DR

This paper explores conditions under which tripartite quantum states formed from entanglement-breaking subspaces are genuinely entangled, providing new insights into multipartite entanglement and its applications.

Contribution

It establishes that tripartite states from entanglement-breaking bipartite states are genuinely entangled, advancing understanding of entanglement structure and supporting multipartite state construction.

Findings

Tripartite states are genuinely entangled when derived from entanglement-breaking subspaces.

Results support a conjecture related to the structure of entangled states.

Constructed states have additive entanglement of formation and are distillable across all bipartitions.

Abstract

The determination of genuine entanglement is a central problem in quantum information processing. We investigate the tripartite state as the tensor product of two bipartite entangled states by merging two systems. We show that the tripartite state is a genuinely entangled state when the range of both bipartite states are entanglement-breaking subspaces. We further investigate the tripartite state when one of the two bipartite states has rank two. Our results provide the latest progress on a conjecture proposed in the paper [Yi Shen $\textit{et al}$, J. Phys. A 53, 125302 (2020)]. We apply our results to construct multipartite states whose bipartite reduced density operators have additive EOF. Further, such states are distillable across every bipartition under local operations and classical communications.