U. Leonhardt et I. Jex, WIGNER FUNCTIONS AND QUADRATURE DISTRIBUTIONS FOR QUANTUM-OSCILLATOR STATES WITH RANDOM-PHASE, Physical review. A, 49(3), 1994, pp. 180001555-180001557
Applying a result of Vogel and Risken [Phys. Rev. A 40, 2847 (1989)] t
o quantum-oscillator states with random phase, we found surprisingly s
imple integral relations between the Wiper function and the quadrature
distribution. In particular, we have shown that the balance of increa
sing and decreasing sections of the quadrature distribution decides th
e sign of the Wiper function.