Concentrating partial entanglement by local operations.

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 EinsteinPodolsky-Rosen singlets, similarly shared between the two observers. The concentration process asymptotically conserves 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. PACS numbers: 03.65.Bz, 42.50.Dv, 89.70.+c