  Entanglement distribution task encounters a problem of how the initial
entangled state should be prepared in order to remain entangled the longest
possible time when subjected to local noises. In the realm of
continuous-variable states and local Gaussian channels it is tempting to assume
that the optimal initial state with the most robust entanglement is Gaussian
too; however, this is not the case. Here we prove that specific non-Gaussian
two-mode states remain entangled under the effect of deterministic local
attenuation or amplification (Gaussian channels with the attenuation
factor/power gain $\kappa_i$ and the noise parameter $\mu_i$ for modes $i=1,2$)
whenever $\kappa_1 \mu_2^2 + \kappa_2 \mu_1^2 < \frac{1}{4}(\kappa_1 +
\kappa_2) (1 + \kappa_1 \kappa_2)$, which is a strictly larger area of
parameters as compared to where Gaussian entanglement is able to tolerate
noise. These results shift the ``Gaussian world'' paradigm in quantum
information science (within which solutions to optimization problems involving
Gaussian channels are supposed to be attained at Gaussian states).
