Three-qubit quantum error-correction scheme for collective decoherence

We show a way to correct collective error through a three-qubit quantum code. The encoding and decoding (i.e., error recovery) operations for such a code, which protects one qubit of quantum information perfectly (with infinite ''distance'') against collective decoherence, are presented. The code is actually a manifestation of a noiseless subsystem first reported by Knill, Laflamme, and Viola [Phys. Rev. Lett. 84, 2525 (2000)], and provides a good illustration of the relationship between noiseless subsystems and error-correcting codes already noted by these authors. We also show in detail how this code can be used to preserve an arbitrary joint state (including entangled states) of two qubits, by pairing each of them with two other qubits, even in the case in which the two resulting clusters interact in nonequivalent ways with a common environment.