Monogamy and Polygamy of Entanglement in Multipartite Quantum Systems

One distinct property of quantum entanglement from other classical correlations is that multipartite entanglements cannot be freely shared among the parties: If two parties in a multi-party system share a maximally entangled state, then they cannot share any entanglement with the rest. This is known as monogamy of entanglement (MoE) [1], which is a key ingredient for secure quantum cryptography [2, 3], and it also plays an important role in condensed-matter physics such as the N -representability problem for fermions [4]. Whereas MoE is the restricted sharability of multipartite entanglement, quantifying entanglement itself is about bipartite entanglement among the parties in multipartite systems. Thus, it is important and necessary to have a proper way of quantifying bipartite entanglement for a good description of the multipartite entanglement monogamy. For this reason, certain criteria of bipartite entanglement measure were recently proposed for a good description of the monogamy nature of entanglement in multipartite quantum systems [5]: