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We consider two classes of non-Gaussian entangled states generated from theproduct of number states with the action of the beamsplitter or the two-modesqueezer. It is shown that, for many of these states, the covariance matrix iscompatible with the covariance matrix of separable Gaussian states and theirseparability cannot be verified by the measurements of the first and secondmoments of canonical variables. We identify a couple of continuous-variableentanglement criteria with higher order moments to verify these non-Gaussianentanglement.

Photonic families of non-Gaussian entangled states and entanglement criteria for continuous-variable systems