  The notion of weak-degradability of quantum channels is introduced by
generalizing the degradability definition given by Devetak and Shor. Exploiting
the unitary equivalence with beam-splitter/amplifier channels we then prove
that a large class of one-mode Bosonic Gaussian channels are either weakly
degradable or anti-degradable. In the latter case this implies that their
quantum capacity Q is null. In the former case instead, this allows us to
establish the additivity of the coherent information for those maps which admit
unitary representation with single-mode pure environment.
