Noiseless Quantum Codes

In this paper we study a model quantum register $\cal R$ made of $N$ replicas (cells) of a given finite-dimensional quantum system S. Assuming that all cells are coupled with a common environment with equal strength we show that, for $N$ large enough, in the Hilbert space of $\cal R$ there exists a linear subspace ${\cal C}_N$ which is dynamically decoupled from the environment. The states in ${\cal C}_N$ evolve unitarily and are therefore decoherence-dissipation free. The space ${\cal C}_N$ realizes a noiseless quantum code in which information can be stored, in principle, for arbitrarily long time without being affected by errors.