be very difficult to reconstruct the off diagonal elements of the density matrix in practical circumstances. However, at least as a matter of principle, one could indeed reconstruct such terms (the evolution of the whole system remains unitary [@omnes]).

Our mechanism of fundamental decoherence could contribute to the understanding of this issue. In the usual system-environment interaction the off-diagonal terms of the density matrix oscillate as a function of time. Since the environment is usually considered to contain a very large number of degrees of freedom, the common period of oscillation for the off-diagonal terms to recover non-vanishing values is very large, in many cases larger than the life of the universe. This allows to consider the problem solved in practical terms. When one adds in the effect we discussed, since it suppresses exponentially the off-diagonal terms, one never has the possibility that the off-diagonal terms will see their initial values restored, no matter how long one waits.

More generally, the environment-induced decoherence leads naturally to a reduced density matrix for the quantum system plus the measurement apparatus that is approximately diagonal and therefore very similar to a statistical mixture of pure states corresponding to different outcomes of the measurement. 