Mixed State Entanglement of Assistance and the Generalized Concurrence

Abstract

We consider the maximum bipartite entanglement that can be distilled from a single copy of a multipartite mixed entangled state, where we focus mostly on $d\times d\times n$-dimensional tripartite mixed states. We show that this {\em assisted entanglement}, when measured in terms of the generalized concurrence (named G-concurrence) is (tightly) bounded by an entanglement monotone, which we call the G-concurrence of assistance. The G-concurrence is one of the possible generalizations of the concurrence to higher dimensions, and for pure bipartite states it measures the {\em geometric mean} of the Schmidt numbers. For a large (non-trivial) class of $d\times d$-dimensional mixed states, we are able to generalize Wootters formula for the concurrence into lower and upper bounds on the G-concurrence. Moreover, we have found an explicit formula for the G-concurrence of assistance that generalizes the expression for the concurrence of assistance for a large class of $d\times d\times n$ dimensional tripartite pure states.