Generalized multiplicative domains and quantum error correction
- Autores: Nathaniel Jonhston, David W. Kribs
- Localización: Proceedings of the American Mathematical Society, ISSN 0002-9939, Vol. 139, Nº 2, 2011, págs. 627-639
- Idioma: inglés
- DOI: 10.1090/s0002-9939-2010-10556-7
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Resumen
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.
