Entanglement of Collaboration

The entanglement of collaboration (EoC) quantifies the maximum amount of entanglement, that can be generated between two parties, A and B, given collaboration with N-2 other parties, when the N parties share a multipartite (possibly mixed) state and where the collaboration consists of local operations and classical communication (LOCC) by all parties. The localizable entanglement (LE) is defined similarly except that A and B do not participate in the effort to generate bipartite entanglement. We compare between these two operational definitions and find sufficient conditions for which the EoC is equal to the LE. In particular, we find that the two are equal whenever they are measured by the concurrence or by one of its generalizations called the G-concurrence. We also find a simple expression for the LE in terms of the Jamiolkowski isomorphism and prove that it is convex.