Stabilizing Quantum Information

The algebraic structure underlying all the schemes for quantum information stabilization is argued to be fully contained in the reducibility of the operator algebra describing the interaction with the environment of the coding quantum system. This property amounts to the existence of a non-trivial group of symmetries for the global dynamics. We provide a unified framework which allows us to build sistematically new classes of (non-additive) error correcting codes and noiseless subsystems. Moreover relations between noiseless subsystems (and codes) and decoupling strategies are clarified.