Reversible Combination of Inequivalent Kinds of Multipartite Entanglement

Abstract

We present a family of tripartite entangled states that, in an asymptotical sense, can be reversibly converted into Einstein-Podolsky-Rosen (EPR) states, shared by parties B and C, and tripartite Greenberger-Horne-Zeilinger (GHZ) states. Thus we show that a bipartite and a genuine tripartite entanglement can be reversibly combined in a tripartite state. For such states the corresponding fractions of GHZ and EPR states represent a complete quantification of their (asymptotical) entanglement resources. More generally, we show that AB, AC, and BC EPR entanglement and GHZ entanglement can be reversibly combined in a single tripartite state. Finally, we generalize this result to any number of parties.