Process output nonclassicality and nonclassicality depth of quantum-optical channels

We introduce a quantum-optical notion of nonclassicality that we call as the process output nonclassicality for multimode quantum channels. The motivation comes from an information-theoretic point of view and the emphasis is on the output states of a channel. We deem a channel to be `classical' if its outputs are always classical irrespective of the input, i.e., if the channel is nonclassicality breaking, and nonclassical otherwise. Our condition is stronger than the one considered by Rahimi-Keshari et al. [PRL {\bf 110}, 160401 (2013)] and we compare the two approaches. Using our framework we then quantify the nonclassicality of a quantum process by introducing a noise-robustness type of measure that we call as the nonclassicality depth of a channel. It characterizes a certain threshold noise beyond which a given channel outputs only classical states. We achieve this by generalizing a prescription by Lee [PRA {\bf 44}, R2775 (1991)] to multimode states and then by extension to multimode channels.