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Currently available separability criteria for continuous-variable states aregenerally based on the covariance matrix of quadrature operators. Thewell-known separability criterion of Duan et al. [Phys. Rev. Lett. 84, 2722(2000)] and Simon [Phys. Rev. Lett. 84, 2726 (2000)] , for example, gives anecessary and sufficient condition for a two-mode Gaussian state to beseparable, but leaves many entangled non-Gaussian states undetected. Here, weintroduce an improvement of this criterion that enables a stronger entanglementdetection. The improved condition is based on the knowledge of an additionalparameter, namely the degree of Gaussianity, and exploits a connection withGaussianity-bounded uncertainty relations [Phys. Rev. A 86, 030102 (2012)]. Weexhibit families of non-Gaussian entangled states whose entanglement remainsundetected by the Duan-Simon criterion.

Detection of non-Gaussian entangled states with an improved continuous-variable separability criterion