Quasi-probability distribution Q(α, α*) versus phase distribution P(θ) in a description of superpositions of coherent states

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