  We present a framework for studying bosonic non-Gaussian channels of
continuous-variable systems. Our emphasis is on a class of channels that we
call photon-added Gaussian channels, which are experimentally viable with
current quantum-optical technologies. A strong motivation for considering these
channels is the fact that it is compulsory to go beyond the Gaussian domain for
numerous tasks in continuous-variable quantum information processing such as
entanglement distillation from Gaussian states and universal quantum
computation. The single-mode photon-added channels we consider are obtained by
using two-mode beam splitters and squeezing operators with photon addition
applied to the ancilla ports giving rise to families of non-Gaussian channels.
For each such channel, we derive its operator-sum representation, indispensable
in the present context. We observe that these channels are Fock preserving
(coherence nongenerating). We then report two examples of activation using our
scheme of photon addition, that of quantum-optical nonclassicality at outputs
of channels that would otherwise output only classical states and of both the
quantum and private communication capacities, hinting at far-reaching
applications for quantum-optical communication. Further, we see that noisy
Gaussian channels can be expressed as a convex mixture of these non-Gaussian
channels. We also present other physical and information-theoretic properties
of these channels.
