Mixed-state entanglement of assistance and the generalized concurrence

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×d×n)-dimensional tripartite mixed states. We show that this assisted entanglement, when measured in terms of the generalized concurrence (called the 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 geometric mean of the Schmidt numbers. For a large (nontrivial) class of (d×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×d×n)-dimensional tripartite pure states.