  The Glauber-Sudarshan diagonal `weight' function provides a natural divide
between the quantum-optical notion of classical and nonclassical states of
continuous variables systems. Based on this demarcation, a channel is said to
be nonclassicality breaking if it outputs only classical states for any input
state. We focus on multimode bosonic Gaussian channels and classify those that
are nonclassicality breaking by introducing a criterion that needs to be
satisfied by the matrices representing these channels. The criterion can be
interpreted as a nonclassicality benchmark for these channels since it
quantifies the threshold noise at which there is a complete nonclassical to
classical transition of the output states, i.e., it quantifies the robustness
of the nonclassicality of the outputs of the channel against Gaussian noise. We
then prove a striking `duality' between nonclassicality breaking and
entanglement breaking bosonic Gaussian channels.
