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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Generalized multiplicative domains and quantum error correction
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by Nathaniel Johnston and David W. Kribs
Proc. Amer. Math. Soc. 139 (2011), 627-639
DOI: https://doi.org/10.1090/S0002-9939-2010-10556-7
Published electronically: July 26, 2010
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Abstract:

Given a completely positive map, we introduce a set of algebras that we refer to as its generalized multiplicative domains. These algebras are generalizations of the traditional multiplicative domain of a completely positive map, and we derive a characterization of them in the unital, trace-preserving case, in other words the case of unital quantum channels, that extends Choi’s characterization of the multiplicative domains of unital maps. We also derive a characterization that is in the same flavour as a well-known characterization of bimodules, and we use these algebras to provide a new representation-theoretic description of quantum error-correcting codes that extends previous results for unitarily-correctable codes, noiseless subsystems and decoherence-free subspaces.
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Bibliographic Information
  • Nathaniel Johnston
  • Affiliation: Department of Mathematics & Statistics, University of Guelph, Guelph, ON, Canada N1G 2W1
  • David W. Kribs
  • Affiliation: Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
  • Received by editor(s): July 20, 2009
  • Received by editor(s) in revised form: March 17, 2010
  • Published electronically: July 26, 2010
  • Communicated by: Marius Junge
  • © Copyright 2010 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 139 (2011), 627-639
  • MSC (2010): Primary 46L05, 47L05, 46N50
  • DOI: https://doi.org/10.1090/S0002-9939-2010-10556-7
  • MathSciNet review: 2736344