The generation of discrete superpositions of coherent states in the anharmonic oscillator model is discussed from the point of view of their quasi-probability distribution Q(a, a*) and phase probability distribution P(O). It is shown that for the superposition with well-distinguishable states both distributions show the same rotational symmetry. The maximum number of well-distinguishable states is estimated. The two functions are illustrated graphically to show explicitly their symmetry and the

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... influence of the interference terms. The similarity between the Q function integrated over the amplitude and the phase distribution P(0) is shown to exist for the anharmonic oscillator states.