Maximal extension on converse monogamy of entanglement for tripartite pure states

TL;DR

This paper extends the understanding of the converse monogamy of entanglement in tripartite pure states, establishing maximal conditions under broader hierarchies of entanglement criteria.

Contribution

It generalizes previous results on converse monogamy of entanglement, showing their maximality within broader hierarchical conditions.

Findings

Extended the conditions for converse monogamy of entanglement.

Proved the maximality of these extensions within the considered hierarchies.

Broadened the theoretical framework for entanglement sharing constraints.

Abstract

Unlike classical correlations, entanglement cannot be freely shared among multiple parties. This unique feature of quantum systems is known as the monogamy of entanglement. While it holds for all multipartite pure states, its converse -- weak entanglement between two parties enforces strong entanglement with a third party -- occurs only under specific conditions. In particular, Hayashi and Chen [Phys. Rev. A \textbf{84}, 012325 (2011)] demonstrated a qualitative version of the converse monogamy of entanglement (CMoE) for tripartite pure states by employing a hierarchy of bipartite entanglement defined through the relations among various separability criteria, and Singh and Datta [IEEE Trans. Inf. Theory \textbf{69}, 6564 (2023)] later extended this notion of the CMoE from the viewpoint of distillability under one-way or two-way classical communication. In this work, we extend their results to the CMoE with broader conditions, and furthermore show that our extensions are maximal with respect to the hierarchies they considered.