Robustness of distributed nonclassicality against local Gaussian noise

We study the robustness of single-mode squeezing nonclassicality against the action of single-mode Gaussian noise (Gaussian channels), first in its local single-mode form and second in its nonlocal distributed form as two-mode entanglement, with the channel acting locally on the single-mode. We find that the distributed single-mode nonclassicality is more robust than local single-mode nonclassicality against the local application of the canonical single-mode Gaussian channels i.e., for the canonical attenuator channel, the canonical amplifier channel, the canonical phase-conjugation channel, and the channel with a singular X matrix, with the exception of the channel with a singular Y matrix. This robustness persists even when the canonical channel is nonclassicality breaking For the canonical channel with a singular Y matrix, we find that the distributed as well as the local single-mode nonclassicality is equally robust against the local application of the channel. We illustrate examples where local single-mode squeezing is more robust than distributed squeezing against the local application of the channel, for channels not of the canonical form.