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Title: Entanglement of assistance and multipartite state distillation

Abstract

We find that the asymptotic entanglement of assistance of a general bipartite mixed state is equal to the smaller of its two local entropies. Our protocol gives rise to the asymptotically optimal Einstein-Podolsky-Rosen (EPR) pair distillation procedure for a given tripartite pure state, and we show that it actually yields EPR and Greenberger-Horne-Zeilinger (GHZ) states; in fact, under a restricted class of protocols, which we call ''one-way broadcasting,'' the GHZ rate is shown to be optimal. This result implies a capacity theorem for quantum channels where the environment helps transmission by broadcasting the outcome of an optimally chosen measurement. We discuss generalizations to m parties and show (for m=4) that the maximal amount of entanglement that can be localized between two parties is given by the smallest entropy of a group of parties of which the one party is a member, but not the other. This gives an explicit expression for the asymptotic localizable entanglement and shows that any nontrivial ground state of a spin system can be used as a perfect quantum repeater if many copies are available in parallel. Finally, we provide evidence that any unital channel is asymptotically equivalent to a mixture of unitaries and any generalmore » channel to a mixture of partial isometries.« less

Authors:
 [1];  [2];  [3];  [4]
  1. IBM T. J. Watson Research Center, Yorktown Heights, New York 10598 (United States)
  2. Institute for Quantum Information, Caltech 107-81, Pasadena, California 91125 (United States)
  3. (Germany)
  4. Department of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW (United Kingdom)
Publication Date:
OSTI Identifier:
20786469
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. A; Journal Volume: 72; Journal Issue: 5; Other Information: DOI: 10.1103/PhysRevA.72.052317; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; CAPACITY; ENTROPY; GROUND STATES; MIXED STATE; MIXTURES; QUANTUM ENTANGLEMENT; QUANTUM MECHANICS; SPIN

Citation Formats

Smolin, John A., Verstraete, Frank, Max-Planck-Institut fuer Quantenoptik, Hans-Kopfermann-Str.1, 85748 Garching, and Winter, Andreas. Entanglement of assistance and multipartite state distillation. United States: N. p., 2005. Web. doi:10.1103/PHYSREVA.72.0.
Smolin, John A., Verstraete, Frank, Max-Planck-Institut fuer Quantenoptik, Hans-Kopfermann-Str.1, 85748 Garching, & Winter, Andreas. Entanglement of assistance and multipartite state distillation. United States. doi:10.1103/PHYSREVA.72.0.
Smolin, John A., Verstraete, Frank, Max-Planck-Institut fuer Quantenoptik, Hans-Kopfermann-Str.1, 85748 Garching, and Winter, Andreas. Tue . "Entanglement of assistance and multipartite state distillation". United States. doi:10.1103/PHYSREVA.72.0.
@article{osti_20786469,
title = {Entanglement of assistance and multipartite state distillation},
author = {Smolin, John A. and Verstraete, Frank and Max-Planck-Institut fuer Quantenoptik, Hans-Kopfermann-Str.1, 85748 Garching and Winter, Andreas},
abstractNote = {We find that the asymptotic entanglement of assistance of a general bipartite mixed state is equal to the smaller of its two local entropies. Our protocol gives rise to the asymptotically optimal Einstein-Podolsky-Rosen (EPR) pair distillation procedure for a given tripartite pure state, and we show that it actually yields EPR and Greenberger-Horne-Zeilinger (GHZ) states; in fact, under a restricted class of protocols, which we call ''one-way broadcasting,'' the GHZ rate is shown to be optimal. This result implies a capacity theorem for quantum channels where the environment helps transmission by broadcasting the outcome of an optimally chosen measurement. We discuss generalizations to m parties and show (for m=4) that the maximal amount of entanglement that can be localized between two parties is given by the smallest entropy of a group of parties of which the one party is a member, but not the other. This gives an explicit expression for the asymptotic localizable entanglement and shows that any nontrivial ground state of a spin system can be used as a perfect quantum repeater if many copies are available in parallel. Finally, we provide evidence that any unital channel is asymptotically equivalent to a mixture of unitaries and any general channel to a mixture of partial isometries.},
doi = {10.1103/PHYSREVA.72.0},
journal = {Physical Review. A},
number = 5,
volume = 72,
place = {United States},
year = {Tue Nov 15 00:00:00 EST 2005},
month = {Tue Nov 15 00:00:00 EST 2005}
}