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We propose a non-Gaussianity measure of a multimode quantum state based onthe negentropy of quadrature distributions. Our measure satisfies desirableproperties as a non-Gaussianity measure, i.e., faithfulness, invariance underGaussian unitary operations, and monotonicity under Gaussian channels.Furthermore, we find a quantitative relation between our measure and thepreviously proposed non-Gaussianity measures defined via quantum relativeentropy and the quantum Hilbert-Schmidt distance. This allows us to estimatethe non-Gaussianity measures readily by homodyne detection, which wouldotherwise require a full quantum-state tomography.

Quantifying non-Gaussianity of a quantum state by the negative entropy of quadrature distributions