Quantum non-Gaussianity of single-mode Schrodinger cat states based on Kurtosis

We evaluate the non-Gaussianity of single-mode Schrodinger cat states based on measure of the kurtosis. It is found that for odd Schrodinger cat state, its kurtosis is always negative, whereas the kurtosis of even Schrodinger cat state may be negative or positive. We then introduce the average kurtosis to measure how far the distribution of Schrodinger cat states is from their corresponding Gaussian ones. Finally, we discuss the relation between the non-Gaussianity and nonclassicality of such states.