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The Quantum Capacity With Symmetric Side Channels

Smith, Graeme and Smolin, John A. and Winter, Andreas (2008) The Quantum Capacity With Symmetric Side Channels. IEEE Transactions on Information Theory, 54 (9). pp. 4208-4217. ISSN 0018-9448.

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In this paper, we present an upper bound for the quantum channel capacity that is both additive and convex. Our bound can be interpreted as the capacity of a channel for high-fidelity quantum communication when assisted by a family of channels that have no capacity on their own. This family of assistance channels, which we call symmetric side channels, consists of all channels mapping symmetrically to their output and environment. The bound seems to be quite tight, and for degradable quantum channels, it coincides with the unassisted channel capacity. Using this symmetric side channel capacity, we find new upper bounds on the capacity of the depolarizing channel. We also briefly indicate an analogous notion for distilling entanglement using the same class of (one-way) channels, yielding one of the few entanglement measures that is monotonic under local operations with one-way classical communication (1-LOCC), but not under the more general class of local operations with classical communication (LOCC).

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Additional Information:© Copyright 2008 IEEE. Reprinted with permission. Manuscript received August 10, 2006; revised March 12, 2008. Published August 27, 2008 (projected). [Date Published in Issue: 2008-08-26 ] The work of G. Smith was supported by the U.S. National Science Foundation under Project PHY-0456720 and by the National Sciences and Engineering Research Council (NSERC) of Canada. The work of J. Smolin was supported by the Army Research Office (ARO) Contract DAAD19-01-C-0056. The work of A. Winter was supported by the U.K. Engineering and Physical Sciences Research Council (EPSRC) via “Quantum Information processing Interdisciplinary research Collaboration (QIP IRC)”, by the European Commission under Project “QAP” (Contract IST-2005-15848), and by a University of Bristol Research Fellowship. The authors would like to thank A. Childs, M.-B. Ruskai, and F. Verstraete for illuminating conversations about degradable channels and symmetric assistance.
Funding AgencyGrant Number
National Science FoundationPHY-0456720
Natural Sciences and Engineering Research Council of Canada (NSERC)UNSPECIFIED
Army Research OfficeDAAD19-01-C-0056
Engineering and Physical Sciences Research Council (EPSRC) (U.K.)QIP IRC
European CommissionIST-2005-15848
University of BristolUNSPECIFIED
Subject Keywords:Entanglement, quantum channel capacity, quantum communication
Issue or Number:9
Record Number:CaltechAUTHORS:SMIieeetit08
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:11796
Deposited By: Archive Administrator
Deposited On:29 Sep 2008 23:00
Last Modified:03 Oct 2019 00:22

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