  We investigate the capacity of bosonic quantum channels for the transmission
of quantum information. Achievable rates are determined from measurable moments
of the channel by showing that every channel can asymptotically simulate a
Gaussian channel which is characterized by second moments of the initial
channel. We calculate the quantum capacity for a class of Gaussian channels,
including channels describing optical fibers with photon losses, by proving
that Gaussian encodings are optimal. Along the way we provide a complete
characterization of degradable Gaussian channels and those arising from
teleportation protocols.
