## Generalized Multiplicative Domains and Quantum Error Correction

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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Cite as:

• N. Johnston and D. W. Kribs, Generalized Multiplicative Domains and Quantum Error Correction. Proceedings of the American Mathematical Society 139, 627–639 (2011).

Related Publications:

Journal of Physics A: Mathematical and Theoretical {\bf 42} 245303 (2009)