Quantum Error Correction and Reversible Operations

Abstract

This article gives a pedagogical account of Shor's nine-bit code for correcting arbitrary errors on single qubits and reviews work that determines when it is possible to maintain quantum coherence by reversing the deleterious effects of open-system quantum dynamics. The review provides an opportunity to introduce an efficient formalism for handling superoperators. Some bounds on entanglement fidelity, which might prove useful in analyses of approximate error correction, are presented and proved.