  We propose a non-Gaussianity measure of a multimode quantum state based on
the negentropy of quadrature distributions. Our measure satisfies desirable
properties as a non-Gaussianity measure, i.e., faithfulness, invariance under
Gaussian unitary operations, and monotonicity under Gaussian channels.
Furthermore, we find a quantitative relation between our measure and the
previously proposed non-Gaussianity measures defined via quantum relative
entropy and the quantum Hilbert-Schmidt distance. This allows us to estimate
the non-Gaussianity measures readily by homodyne detection, which would
otherwise require a full quantum-state tomography.
