Noiseless Quantum Codes

In this paper we study a model quantum register 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 R there exists a linear subspace C₍ which is dynamically decoupled from the environment. The states in C₍ evolve unitarily and are therefore decoherence-dissipation free. The space C₍ realizes a noiseless quantum code in which information can be stored, in principle, for an arbitrarily long time without being affected by errors.