  We show that the theory of operator quantum error correction can be naturally
generalized by allowing constraints not only on states but also on observables.
The resulting theory describes the correction of algebras of observables (and
may therefore suitably be called ``operator algebra quantum error
correction''). In particular, the approach provides a framework for the
correction of hybrid quantum-classical information and it does not require the
state to be entirely in one of the corresponding subspaces or subsystems. We
discuss applications to quantum teleportation and to the study of information
flows in quantum interactions.
