Concentrating partial entanglement by local operations

Phys. Rev. A 53, 2046 – Published 1 April 1996
Charles H. Bennett, Herbert J. Bernstein, Sandu Popescu, and Benjamin Schumacher


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 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. © 1996 The American Physical Society.


  • Received 9 August 1995
  • Published in the issue dated April 1996

© 1996 The American Physical Society

Authors & Affiliations

Charles H. Bennett

  • IBM Research Division, T. J. Watson Center, Yorktown Heights, New York 10598

Herbert J. Bernstein

  • Hampshire College and Institute for Science and Interdisciplinary Studies, Amherst, Massachusetts 01002

Sandu Popescu

  • Physics Department, Tel Aviv University, Tel Aviv, Israel

Benjamin Schumacher

  • Physics Department, Kenyon College, Gambier, Ohio 43022

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