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Entanglement of assistance and multipartite state distillation

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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 general channel to a mixture of partial isometries.
Keywords
NOISY QUANTUM CHANNELS, CLASSICAL INFORMATION, ERROR-CORRECTION, STRONG, CONVERSE, CODING THEOREM, DENSITY-MATRIX, CAPACITY, SYSTEMS, ENTROPY, COST

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MLA
Smolin, JA, Frank Verstraete, and A Winter. “Entanglement of Assistance and Multipartite State Distillation.” PHYSICAL REVIEW A 72.5 (2005): n. pag. Print.
APA
Smolin, J., Verstraete, F., & Winter, A. (2005). Entanglement of assistance and multipartite state distillation. PHYSICAL REVIEW A, 72(5).
Chicago author-date
Smolin, JA, Frank Verstraete, and A Winter. 2005. “Entanglement of Assistance and Multipartite State Distillation.” Physical Review A 72 (5).
Chicago author-date (all authors)
Smolin, JA, Frank Verstraete, and A Winter. 2005. “Entanglement of Assistance and Multipartite State Distillation.” Physical Review A 72 (5).
Vancouver
1.
Smolin J, Verstraete F, Winter A. Entanglement of assistance and multipartite state distillation. PHYSICAL REVIEW A. 2005;72(5).
IEEE
[1]
J. Smolin, F. Verstraete, and A. Winter, “Entanglement of assistance and multipartite state distillation,” PHYSICAL REVIEW A, vol. 72, no. 5, 2005.
@article{8593965,
  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 general channel to a mixture of partial isometries.},
  articleno    = {052317},
  author       = {Smolin, JA and Verstraete, Frank and Winter, A},
  issn         = {2469-9926},
  journal      = {PHYSICAL REVIEW A},
  keywords     = {NOISY QUANTUM CHANNELS,CLASSICAL INFORMATION,ERROR-CORRECTION,STRONG,CONVERSE,CODING THEOREM,DENSITY-MATRIX,CAPACITY,SYSTEMS,ENTROPY,COST},
  language     = {eng},
  number       = {5},
  pages        = {10},
  title        = {Entanglement of assistance and multipartite state distillation},
  url          = {http://dx.doi.org/10.1103/PhysRevA.72.052317},
  volume       = {72},
  year         = {2005},
}

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