  The newfound importance of ``entanglement as a resource'' in quantum
computation and quantum communication compels us to quantify it in as many
distinct ways as possible. Here we explore a new measure of entanglement for
mixed quantum states of bipartite systems, which we name the Entanglement of
Assistance. We show it to be the maximum average entanglement of all pure-state
ensembles consistent with the given density matrix. In this sense, the
Entanglement of Assistance is a quantity directly dual to the more standard
Entanglement of Formation. With the help of lower and upper bounds, we
calculate the Entanglement of Assistance for a few cases and use these results
to show that it possesses the surprising property of superadditivity. We
believe that this may shed some light on the question of additivity for the
Entanglement of Formation.
