We present a unified approach to quantum error correction, called operator quantum error correction. Our scheme relies on a generalized notion of a noiseless subsystem that is investigated here. By combining the active error correction with this generalized noiseless subsystems method, we arrive at a unified approach which incorporates the known techniques—i.e., the standard error correction model, the method of decoherence-free subspaces, and the noiseless subsystem method—as special cases. Moreover, we demonstrate that the quantum error correction condition from the standard model is a necessary condition for all known methods of quantum error correction.

• Received 9 December 2004

DOI:https://doi.org/10.1103/PhysRevLett.94.180501