Non-distillable entanglement guarantees distillable entanglement

TL;DR

This paper explores the relationship between non-distillable and distillable entanglement in tripartite quantum systems, revealing a converse monogamy property and classifying states based on their bipartite entanglement characteristics.

Contribution

It introduces a novel classification of tripartite pure states based on bipartite reduced density operators, offering a new approach to understanding entanglement structure.

Findings

Non-distillable entanglement implies the existence of distillable entanglement with the third party.

Classified states' structure is systematically characterized and generated.

Results extend to multipartite quantum states.

Abstract

The monogamy of entanglement is one of the basic quantum mechanical features, which says that when two partners Alice and Bob are more entangled then either of them has to be less entangled with the third party. Here we qualitatively present the converse monogamy of entanglement: given a tripartite pure system and when Alice and Bob are entangled and non-distillable, then either of them is distillable with the third party. Our result leads to the classification of tripartite pure states based on bipartite reduced density operators, which is a novel and effective way to this long-standing problem compared to the means by stochastic local operations and classical communications. Furthermore we systematically indicate the structure of the classified states and generate them. We also extend our results to multipartite states.