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Entanglement of assistance and multipartite state distillation

Smolin, John A. and Verstraete, Frank and Winter, Andreas (2005) Entanglement of assistance and multipartite state distillation. Physical Review A, 72 (5). Art. no. 052317. ISSN 1050-2947. doi:10.1103/PhysRevA.72.052317.

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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.

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Additional Information:© 2005 The American Physical Society (Received 10 June 2005; published 17 November 2005) We wish to thank Charles H. Bennett, Ignacio Cirac, Igor Devetak, Mark Fannes, Michał Horodecki, Debbie Leung, Jonathan Oppenheim, and Tobias Osborne for interesting discussions on the entanglement of assistance and unital channels and especially Berry Groisman, Noah Linden, and Sandu Popescu for sharing their results in [4] prior to publication. J.A.S. acknowledges the support of the NSA and ARO under Contract No. DAAD19-01-C-0056. A.W. is supported by the EU project RESQ (Contract no. IST-2001-37559) and by the U.K. Engineering and Physical Sciences Research Council’s “IRC QIP.” The hospitality of the Isaac Newton Institute of Mathematical Sciences, Cambridge, during the topical semester on Quantum Information Sciences (16/08-17/12 2004) is gratefully acknowledged by J.A.S. and A.W. F.V. acknowledges support by the Gordon and Betty Moore Foundation (the Information Science and Technology Initiative, Caltech).
Funding AgencyGrant Number
National Security Agency (NSA)UNSPECIFIED
Army Research OfficeDAAD19-01-C-0056
European Union (EU)IST-2001-37559
Engineering and Physical Sciences Research Council (EPSRC)UNSPECIFIED
Gordon and Betty Moore FoundationUNSPECIFIED
Issue or Number:5
Record Number:CaltechAUTHORS:SMOpra05
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:1530
Deposited By: Archive Administrator
Deposited On:27 Jan 2006
Last Modified:08 Nov 2021 19:11

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