  If two separated observers are supplied with entanglement, in the form of $n$
pairs of particles in identical partly-entangled pure states, one member of
each pair being given to each observer; they can, by local actions of each
observer, concentrate this entanglement into a smaller number of
maximally-entangled pairs of particles, for example Einstein-Podolsky-Rosen
singlets, similarly shared between the two observers. The concentration process
asymptotically conserves {\em entropy of entanglement}---the von Neumann
entropy of the partial density matrix seen by either observer---with the yield
of singlets approaching, for large $n$, the base-2 entropy of entanglement of
the initial partly-entangled pure state. Conversely, any pure or mixed
entangled state of two systems can be produced by two classically-communicating
separated observers, drawing on a supply of singlets as their sole source of
entanglement.
