Coauthors: Richard MacKenzie

Decoherence provides an elegant framework to explain why an open quantum system coupled to its environment will exhibit a set of preferred states, usually ruling out a coherent superposition of arbitrary states. This framework relies essentially on the interaction between the system and its environment. In the simplest model of decoherence, it was readily realized that there exist initial state of the environment that allow for decoherence-free unitary evolution of the quantum system.

We investigate the conditions under which such special initial states do exist in a framework where the quantum system interacts with its environment and the environment also evolves by itself. The results obtained underline the crucial role of the environment's self-evolution. The ability to identify those special initial states and to prepare them might be used in order to store quantum states. Indeed, even if the environment cannot be controlled, it might be possible to prepare it in a specific initial state. However, our results restrict what can be expected from such a technique. More precisely, we obtain a mathematical characterization for the existence of an initial state allowing decoherence-free evolution in presence of an interaction hamiltonian and a self-evolution of the environment. This result is stated in terms of the structure of the two hamiltonians. We also present topological evidences that indicate that pairs of hamiltonians allowing for decoherence-free evolution are rare among pairs of hamiltonians.