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Information-preserving structures: A general framework for quantum zero-error information

Blume-Kohout, Robin and Ng, Hui Khoon and Poulin, David and Viola, Lorenza (2010) Information-preserving structures: A general framework for quantum zero-error information. Physical Review A, 82 (6). Art. No. 062306. ISSN 1050-2947. http://resolver.caltech.edu/CaltechAUTHORS:20110315-091122301

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Abstract

Quantum systems carry information. Quantum theory supports at least two distinct kinds of information (classical and quantum), and a variety of different ways to encode and preserve information in physical systems. A system’s ability to carry information is constrained and defined by the noise in its dynamics. This paper introduces an operational framework, using information-preserving structures, to classify all the kinds of information that can be perfectly (i.e., with zero error) preserved by quantum dynamics. We prove that every perfectly preserved code has the same structure as a matrix algebra, and that preserved information can always be corrected.We also classify distinct operational criteria for preservation (e.g., “noiseless,” “unitarily correctible,” etc.) and introduce two natural criteria for measurement-stabilized and unconditionally preserved codes. Finally, for several of these operational criteria, we present efficient (polynomial in the state-space dimension) algorithms to find all of a channel’s information-preserving structures.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1103/PhysRevA.82.062306DOIUNSPECIFIED
http://link.aps.org/doi/10.1103/PhysRevA.82.062306PublisherUNSPECIFIED
http://pra.aps.org/abstract/PRA/v82/i6/e062306PublisherUNSPECIFIED
Additional Information:© 2010 The American Physical Society. Received 27 August 2010; published 7 December 2010. The authors acknowledge support in part by the Gordon and Betty Moore Foundation (D.P. and H-K.N.); by the Natural Sciences and Engineering Research Council of Canada and Fonds Québécois de la Recherche sur la Nature et les Technologies (D.P.); by the National Science Foundation under Grants No. PHY-0803371, No. PHY-0456720, No.PHY-0555417, and No. PHY-0903727 (L.V.); and by the Government of Canada through Industry Canada and the Province of Ontario through the Ministry of Research & Innovation (R.B.K.). We also gratefully acknowledge extensive conversations with Robert Spekkens, Daniel Gottesman, Cedric Beny, and Wojciech Zurek.
Funders:
Funding AgencyGrant Number
Gordon and Betty Moore FoundationUNSPECIFIED
Natural Sciences and Engineering Research Council of Canada (NSERC)UNSPECIFIED
Fonds Québécois de la Recherche sur la Nature et les TechnologiesUNSPECIFIED
NSFPHY-0803371
NSFPHY-0456720
NSFPHY-0555417
NSFPHY-0903727
Government of Canada through Industry CanadaUNSPECIFIED
Province of Ontario through the Ministry of Research & InnovationUNSPECIFIED
Classification Code:PACS: 03.67.Pp, 03.67.Lx, 03.65.Yz, 89.70.-a
Record Number:CaltechAUTHORS:20110315-091122301
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20110315-091122301
Official Citation:Information-preserving structures: A general framework for quantum zero-error information Robin Blume-Kohout, Hui Khoon Ng, David Poulin, and Lorenza Viola Published 7 December 2010 (25 pages) 062306
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:22882
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:15 Mar 2011 22:49
Last Modified:26 Dec 2012 13:03

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