Quantum error correction and reversible operations

This article gives a pedagogical account of Shor's nine-bit code for correc ting arbitrary errors on single qubits and reviews work that determines whe n it is possible to maintain quantum coherence by reversing I:he deleteriou s effects of open-system quantum dynamics. The review provides an opportuni ty to introduce an efficient formalism for handling superoperators. Some bo unds on entanglement fidelity, which might prove useful in analyses of appr oximate error correction, are presented and proved.