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A Decoupling Approach to the Quantum Capacity

Hayden, Patrick and Horodecki, Michał and Winter, Andreas and Yard, Jon (2008) A Decoupling Approach to the Quantum Capacity. Open Systems and Information Dynamics, 15 (1). pp. 7-19. ISSN 1230-1612.

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We give a short proof that the coherent information is an achievable rate for the transmission of quantum information through a noisy quantum channel. Our method is to produce random codes by performing a unitarily covariant projective measurement on a typical subspace of a tensor power state. We show that, provided the rank of each measurement operator is sufficiently small, the transmitted data will, with high probability, be decoupled from the channel environment. We also show that our construction leads to random codes whose average input is close to a product state and outline a modification yielding unitarily invariant ensembles of maximally entangled codes.

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Additional Information:© 2008 World Scientific Publishing Company. Received: November 2, 2007. We would like to thank Alexander Holevo, Debbie Leung, Renato Renner for interesting discussions. PH is supported by the Canada Research Chairs program, CIFAR, FQRNT, MITACS, NSERC and QuantumWorks. He is also grateful to the DAMTP in Cambridge for their hospitality. MH is supported by Polish Ministry of Scientific Research and Information Technology under the (solicited) grant no. PBZ-MIN-008/P03/2003 and EC IP SCALA. AW was supported through an Advanced Research Fellowship of the U.K. EPSRC via the QIP IRC, and the European Commission IP QAP (IST-2005- 015848). JY’s research at LANL is supported by the Center for Nonlinear Studies (CNLS), the Quantum Institute and the LDRD program of the U.S. Department of Energy. He is also grateful for support from the U.S. National Science Foundation under Grant No. PHY-0456720 through Caltech and from the CIFAR when this work was initiated.
Funding AgencyGrant Number
Canada Research Chairs programUNSPECIFIED
Canadian Institute for Advanced Research (CIFAR)UNSPECIFIED
Fonds Québécois de la Recherche sur la Nature et les Technologies (FQRNT)UNSPECIFIED
Mathematics of Information Technology and Complex Systems (MITACS)UNSPECIFIED
Natural Sciences and Engineering Research Council of Canada (NSERC)UNSPECIFIED
Polish Ministry of Scientific Research and Information TechnologyPBZ-MIN-008/P03/2003
Engineering and Physical Sciences Research Council (EPSRC) Advanced Research FellowshipUNSPECIFIED
European CommissionIST-2005-015848
Center for Nonlinear Studies (CNLS)UNSPECIFIED
Department of Energy (DOE) Quantum Institute and the LDRD programUNSPECIFIED
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Record Number:CaltechAUTHORS:20101209-150911246
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:21284
Deposited By: Tony Diaz
Deposited On:14 Dec 2010 20:56
Last Modified:03 Oct 2019 02:22

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