  A complete degradability analysis of one-mode Gaussian Bosonic channels is
presented. We show that apart from the class of channels which are unitarily
equivalent to the channels with additive classical noise, these maps can be
characterized in terms of weak- and/or anti-degradability. Furthermore a new
set of channels which have null quantum capacity is identified. This is done by
exploiting the composition rules of one-mode Gaussian maps and the fact that
anti-degradable channels can not be used to transfer quantum information.
