  We present an upper bound for the Kolmogorov-Sinai entropy of quantum systems
having a mixing quantum phase space. The method for this estimation is based on
the following ingredients: i) the graininess of quantum phase space in virtue
of the Uncertainty Principle, ii) a time rescaled KS-entropy that introduces
the characteristic timescale as a parameter, and iii) the factorization
property of the mixing correlations. The analogy between the structures of the
mixing level of the ergodic hierarchy and of its quantum counterpart is shown.
Moreover, the logarithmic timescale, characteristic of quantum chaotic systems,
is obtained.
