Fading bosonic channels support positive quantum communication rates with non-Gaussian encodings even when thermal states fail, and always allow positive-rate ED and QKD if not completely noisy.
Substituting the decomposition forρ, we obtain: S(ρ) =H 2(p0) + (1−p 0)S(σ),(C3) whereH 2(x) =−xlog 2 x−(1−x) log 2(1−x) is the binary entropy function
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Convex combinations of bosonic pure-loss channels
Fading bosonic channels support positive quantum communication rates with non-Gaussian encodings even when thermal states fail, and always allow positive-rate ED and QKD if not completely noisy.