Algebraic and information-theoretic conditions for operator quantum error-correction

Operator quantum error-correction is a technique for robustly storing quantum information in the presence of noise. It generalizes the standard theory of quantum error-correction, and provides a unified framework for topics such as quantum error-correction, decoherence-free subspaces, and noiseless subsystems. This paper develops (a) easily applied algebraic and information-theoretic conditions which characterize when operator quantum error-correction is feasible; (b) a representation theorem for a class of noise processes which can be corrected using operator quantum error-correction; and (c) generalizations of the coherent information and quantum data processing inequality to the setting of operator quantum error-correction.