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, on e member of each pair being given to each observer, they can, by local actions of each observer, concentrate this entanglement into a smalle r number of maximally entangled pairs of particles, for example, Einst ein-Podolsky-Rosen singlets, similarly shared between the two observer s. The concentration process asymptotically conserves entropy of entan glement-the von Neumann entropy of the partial density matrix seen by either observer-with the yield of singlets approaching, for large n, t he base-2 entropy of entanglement of the initial partly entangled pure state. Conversely, any pure or mixed entangled state of two systems c an be produced by two classically communicating separated observers, d rawing on a supply of singlets as their sole source of entanglement.