Wigner functions and quadrature distributions for quantum-oscillator states with random phase
Ulf Leonhardt, Igor Jex · Physical Review A · 1994
Applying a result of Vogel and Risken [Phys. Rev. A 40, 2847 (1989)] to quantum-oscillator states with random phase, we found surprisingly simple integral relations between the Wigner function and the quadrature distribution. In particular, we have shown that the balance of increasing and decreasing sections of the quadrature distribution decides the sign of the Wigner function.