  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.
