Phase-space-interference approaches employ interference on the phase plane to explain a quantum state’s photon-number distribution. This paper generalizes the approach so that knowledge of the photon-number distribution explains the state’s quantum phase-plane distribution. The required generalization is as follows. The Bohr-Sommerfeld ‘‘band’’ or trajectory of the mixture of number states ∼(‖N〉〈N‖+‖M〉〈M‖) consists of two annuli centered on the origin. In contrast, the trajectory of the pure number state superposition ∼(‖N〉+‖M〉) (with M>N) contains additional interference structures, namely, (M-N) symmetrically positioned radial spokes connecting the annuli. These spokes intersect the circular band attributed to a photon-number state at (M-N) locations, with the resulting destructive interference eliminating states ‖N+1〉 to ‖M-1〉. These structures build state phase-plane quantum probability distributions, as we illustrate for the squeezed vacuum. This state is missing every odd-numbered photon number state, and thus its trajectory consists of a repeated pattern of two heavily emphasized bars eliminating every odd-numbered state. These bars sum to generate the traditional ‘‘cigar’’ shape of the squeezed state.

• Received 31 October 1994

DOI:https://doi.org/10.1103/PhysRevA.51.2715