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Concentrating Partial Entanglement by Local Operations

Charles H. Bennett·Herbert J. Bernstein·Sandu Popescu·Benjamin Schumacher
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Abstract

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.

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Charles H. Bennett, Herbert J. Bernstein, Sandu Popescu, Benjamin Schumacher. 1995-11-21. Concentrating Partial Entanglement by Local Operations. https://doi.org/10.1103/physreva.53.2046

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