  In this work we probe the usefulness of non-Gaussian entangled states as a
resource for quantum communication through atmospheric channels. We outline the
initial conditions in which non-Gaussian state transfer leads to enhanced
entanglement transfer relative to that obtainable via Gaussian state transfer.
However, we conclude that in (anticipated) operational scenarios - where most
of the non-Gaussian states to be transferred over the air are created
just-in-time via photonic subtraction, addition or replacement from incoming
Gaussian states - the entanglement-generation rate between stations via
non-Gaussian state transfer will be substantially less than that created by
direct Gaussian state transfer. The role of post-selection, distillation and
quantum memory in altering this conclusion is discussed, and comparison with
entanglement rates produced via single-photon technologies is provided. Our
results suggest that in the near term entangled Gaussian states, squeezed
beyond some modest level, offer the most attractive proposition for the
distribution of entanglement through high-loss atmospheric channels. The
implications of our results for entanglement-based QKD to low-earth orbit are
presented.
