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

Currently available separability criteria for continuous-variable states are generally based on the covariance matrix of quadrature operators. The well-known separability criterion of Duan et al. [L. M. Duan, Phys. Rev. Lett. 84, 2722 (2000)PRLTAO0031-900710.1103/PhysRevLett.84.2722] and Simon [R. Simon, Phys. Rev. Lett. 84, 2726 (2000)PRLTAO0031-900710.1103/PhysRevLett.84.2726], for example, gives a necessary and sufficient condition for a two-mode Gaussian state to be separable, but leaves many entangled non-Gaussian states undetected. Here we introduce an improvement of this criterion that enables a stronger entanglement detection. The improved condition is based on the knowledge of an additional parameter, namely, the degree of Gaussianity, and exploits a connection with Gaussianity-bounded uncertainty relations [A. Mandilara and N. J. Cerf, Phys. Rev. A 86, 030102 (2012)PLRAAN1050-294710.1103/PhysRevA.86.030102]. We exhibit families of non-Gaussian entangled states whose entanglement remains undetected by the Duan-Simon criterion.