We develop a method for efficiently calculating non-Gaussianity of quantum states in Wigner function representation based on the sine metric. In contradistinction to the known non-Gaussianity measures, we seek the corresponding reference Gaussian counterpart via the cumulant-expansion techniques of quantum state. We analyze this quantity for some non-Gaussian quantum states, which can not be well detected or quantified by other non-Gaussianity measures such as the degree of Gaussianity, the Hilbert-Schmidt metric and the relative entropy metric, thereby providing a good measure to quantify a genuine non-Gaussian state.
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