Generalized Multiplicative Domains and Quantum Error Correction

Details Generalized Multiplicative Domains and Quantum Error Correction Generalized Multiplicative Domains and Quantum Error Correction

2010-04-28

arxiv.org/abs/1004.5112v1

Proc. Amer. Math. Soc. 139 (2011), 627-639

Physics

Quantum Physics

14 pages

Scientific paper

10.1090/S0002-9939-2010-10556-7

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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