Weaker entanglement between two parties guarantees stronger entanglement with a third party

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 an effective way to this longstanding 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. © 2011 American Physical Society.