Quantum-optical channels that output only classical states

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.