  We study the evolution of higher-order nonclassicality and entanglement
criteria in atmospheric fluctuating-loss channels. By formulating input-output
relations for the matrix of moments, we investigate the influence of such
channels on the corresponding quantumness criteria. This generalization of our
previous work on Gaussian entanglement [M. Bohmann et al., Phys. Rev. A 94,
010302(R) (2016)] not only exploits second-order-based scenarios, but it also
provides a detailed investigation of nonclassicality and entanglement in
non-Gaussian and multimode radiation fields undergoing a fluctuating
attenuation. That is, various examples of criteria and states are studied in
detail, unexpected effects, e.g., the dependency of the squeezing transfer on
the coherent displacement, are discovered, and it is demonstrated that
non-Gaussian entanglement can be more robust against atmospheric losses than
Gaussian one. Additionally, we propose a detection scheme for measuring the
considered moments after propagation through the atmosphere. Therefore, our
results may help to develop, improve, and optimize non-Gaussian sources of
quantum light for applications in free-space quantum communication.
