Weaker entanglement guarantees stronger entanglement

TL;DR

This paper introduces a converse to the monogamy of entanglement, showing that weak bipartite entanglement implies strong entanglement with a third party, leading to a new classification of tripartite states.

Contribution

It presents the first qualitative formulation of the converse monogamy of entanglement and proposes a novel classification method for tripartite pure states based on bipartite reduced states.

Findings

Weak bipartite entanglement correlates with strong third-party entanglement.

A new classification scheme for tripartite pure states is developed.

The structure of classified states is systematically characterized.

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 weakly entangled, then either of them is generally strongly entangled 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. We also systematically indicate the structure of the classified states and generate them.