Superior resilience of non-Gaussian entanglement against local Gaussian noises

Abstract

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 $κ_i$ and the noise parameter $μ_i$ for modes $i=1,2$) whenever $κ_1 μ_2^2 + κ_2 μ_1^2 < \frac{1}{4}(κ_1 + κ_2) (1 + κ_1 κ_2)$, 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).