In this paper, the mean photon number, the second-order coherence and the distribution of this optical state are derived and some properties of this state are presented. In general the mean photon number is not equal to the sum of the mean photon number of three elements, the distribution is not equal to the sum of the distribution of three elements. The result shows that whether this optical cat state exists bunching effect or an bunching effect is decided by the eigenvalues, superposition coefficents of coherent states they take part in superpostion and their relation.
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