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.

中文翻译：

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通过正交分布的负熵量化量子态的非高斯性

我们提出了一种基于正交分布的负熵的多模量子态的非高斯度量。我们的度量满足作为非高斯度量的理想特性，即高斯酉运算下的忠实度、不变性和高斯通道下的单调性。此外，我们发现我们的度量与之前提出的通过量子相对熵和量子 Hilbert-Schmidt 距离定义的非高斯度量之间存在定量关系。这使我们能够通过零差检测轻松估计非高斯性度量，否则将需要完整的量子态断层扫描。