Quantum nonlocality without entanglement

Phys. Rev. A 59, 1070 – Published 1 February 1999
Charles H. Bennett, David P. DiVincenzo, Christopher A. Fuchs, Tal Mor, Eric Rains, Peter W. Shor, John A. Smolin, and William K. Wootters


We exhibit an orthogonal set of product states of two three-state particles that nevertheless cannot be reliably distinguished by a pair of separated observers ignorant of which of the states has been presented to them, even if the observers are allowed any sequence of local operations and classical communication between the separate observers. It is proved that there is a finite gap between the mutual information obtainable by a joint measurement on these states and a measurement in which only local actions are permitted. This result implies the existence of separable superoperators that cannot be implemented locally. A set of states are found involving three two-state particles that also appear to be nonmeasurable locally. These and other multipartite states are classified according to the entropy and entanglement costs of preparing and measuring them by local operations.

DOI: http://dx.doi.org/10.1103/PhysRevA.59.1070

  • Received 17 June 1998
  • Published in the issue dated February 1999

© 1999 The American Physical Society

Authors & Affiliations

Charles H. Bennett1, David P. DiVincenzo1, Christopher A. Fuchs2, Tal Mor3, Eric Rains4, Peter W. Shor4, John A. Smolin1, and William K. Wootters5

  • 1IBM Research Division, T. J. Watson Research Center, Yorktown Heights, New York 10598
  • 2Norman Bridge Laboratory of Physics 12-33, California Institute of Technology, Pasadena, California 91125
  • 3Département d’Informatique et de Recherche Opérationelle, Succursale Centre-Ville, Montréal, Canada H3C 3J7
  • 4AT&T Shannon Laboratory, 180 Park Avenue, Building 103, Florham Park, New Jersey 07932
  • 5Physics Department, Williams College, Williamstown, Massachusetts 01267

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