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 EinsteinPodolskyRosen (EPR) pair distillation procedure for a given tripartite pure state, and we show that it actually yields EPR and GreenbergerHorneZeilinger (GHZ) states; in fact, under a restricted class of protocols, which we call ''oneway 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 »
 Authors:
 IBM T. J. Watson Research Center, Yorktown Heights, New York 10598 (United States)
 Institute for Quantum Information, Caltech 10781, Pasadena, California 91125 (United States)
 (Germany)
 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, MaxPlanckInstitut fuer Quantenoptik, HansKopfermannStr.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, MaxPlanckInstitut fuer Quantenoptik, HansKopfermannStr.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, MaxPlanckInstitut fuer Quantenoptik, HansKopfermannStr.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 MaxPlanckInstitut fuer Quantenoptik, HansKopfermannStr.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 EinsteinPodolskyRosen (EPR) pair distillation procedure for a given tripartite pure state, and we show that it actually yields EPR and GreenbergerHorneZeilinger (GHZ) states; in fact, under a restricted class of protocols, which we call ''oneway 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}
}

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Quantum teleportation of an arbitrary twoqubit state and its relation to multipartite entanglement
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Comment on 'Quantum teleportation of an arbitrary twoqubit state and its relation to multipartite entanglement'
The multipartite state in the Rigolin's protocol [Phys. Rev. A 71, 032303 (2005)] for teleporting an arbitrary twoqubit state is just a product state of N EinsteinPodolskyRosen pairs in essence, not a genuine multipartite entangled state, and this protocol in principle is equivalent to the YangGuo protocol [Chin. Phys. Lett. 17, 162 (2000)].