Quantum dynamical entropy and decoherence rate

We investigate quantum dynamical systems defined on a finite-dimensional Hilbert space and subjected to an interaction with an environment. The rate of decoherence of initially pure states, measured by the increase of their von Neumann entropy, averaged over an ensemble of random pure states, is proved to be bounded from above by the partial entropy used to define the ALF-dynamical entropy. The rate of decoherence induced by the sequence of the von Neumann projectors measurements is shown to be maximal, if the measurements are performed in a randomly chosen basis. The numerically observed linear increase of entropies is attributed to free independence of the measured observable and the unitary dynamical map.