  We give a criterion to differentiate between dissipative and diffusive
quantum operations. It is based on the classical idea that dissipative
processes contract volumes in phase space. We define a quantity that can be
regarded as ``quantum phase space contraction rate'' and which is related to a
fundamental property of quantum channels: non-unitality. We relate it to other
properties of the channel and also show a simple example of dissipative noise
composed with a chaotic map. The emergence of attaractor-like structures is
displayed.
