Mixed-state entanglement of assistance and the generalized concurrence
Gilad Gour · Physical Review A · 2005
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 $(d\ifmmode\times\else\texttimes\fi{}d\ifmmode\times\else\texttimes\fi{}n)$-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 $(d\ifmmode\times\else\texttimes\fi{}d)$-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 $(d\ifmmode\times\else\texttimes\fi{}d\ifmmode\times\else\texttimes\fi{}n)$-dimensional tripartite pure states.