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