  A characterization of qubit quantum channels is introduced. In analogy to
what happens in the context of Bosonic channels we exploit the possibility of
representing the states of the system in terms of characteristic function. The
latter are functions of non-commuting variables (Grassmann variables) and are
defined in terms of generalized displacement operators. In this context we
introduce the set of Gaussian channels and show that they share similar
properties with the corresponding Bosonic counterpart.
