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Communicating Over Adversarial Quantum Channels Using Quantum List Codes

Leung, Debbie and Smith, Graeme (2008) Communicating Over Adversarial Quantum Channels Using Quantum List Codes. IEEE Transactions on Information Theory, 54 (2). pp. 883-887. ISSN 0018-9448. https://resolver.caltech.edu/CaltechAUTHORS:LEUieeetit08

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Abstract

In this correspondence, we study quantum communication in the presence of adversarial noise. In this setting, communicating with perfect fidelity requires a quantum code of bounded minimum distance, for which the best known rates are given by the quantum Gilbert–Varshamov (QGV) bound. Asking only for arbitrarily high fidelity and letting the sender and reciever use a secret key of length logarithmic in the number of qubits sent, we find a dramatic improvement over the QGV rates. In fact, our protocols allow high fidelity transmission at noise levels for which perfect fidelity is impossible. To achieve such rates, we introduce fully quantum list codes, which may be of independent interest.


Item Type:Article
Additional Information:© Copyright 2008 IEEE. Reprinted with permission. Manuscript received June 14, 2006; revised July 6, 2007. [Posted online: 2008-01-22] D. Leung acknowledges travel funds from the CIAR to visit IBM, and funding from the Tolman Foundation, CIAR, NSERC, CRC, CFI, and OIT. The work of G. Smith was supported by the U.S. NSF Grant PHY-0456720 and Canada’s NSERC. This work was supported by the U.S. NSF Grant EIA-0086038. The material in this correspondence was presented at the Ninth Workshop on Quantum Information Processing, Paris, France, January 2006. The authors are grateful to Roberto Oliveira, John Smolin, Daniel Gottesman, and especially Aram Harrow for helpful discussions, as well as to the IBM T.J. Watson Research Center, where the bulk of this work was completed.
Subject Keywords:Adversarial channels, approximate quantum codes, quantum error correction, quantum list codes
Issue or Number:2
Record Number:CaltechAUTHORS:LEUieeetit08
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:LEUieeetit08
Alternative URL:http://dx.doi.org/10.1109/TIT.2007.913433
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:9661
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:23 Feb 2008
Last Modified:03 Oct 2019 00:02

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