## 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.## References

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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