FROM THE WIGNER FUNCTION TO THE s-ORDERED PHASE-SPACE DISTRIBUTION VIA A GAUSSIAN NOISE CHANNEL

Various phase-space distributions, from the celebrated Wigner function, to the Husimi Q function and the Glauber-Sudarshan P distribution, have played an interesting and important role in the phase-space formulation of quantum mechanics in general, and quantum optics in particular. A unified approach to all these distributions based on the notion of the 8-ordered phase-space distribution was introduced by Cahill and Glauber. With the intention of illuminating the physical meaning of the parameter s, we interpret the 8-ordered phase-space distribution as the Wigner function of a state under the Gaussian noise channel, and thus reveal an intrinsic connection between the 8-ordered phase-space distribution and the Gaussian noise channel, which yields a physical insight into the 8-ordered phase-space distribution. In this connection, the parameter -s/2 (rather than the original s) acquires the role of the noise occurring in the Gaussian noise channel. An alternative representation of the Gaussian noise channel as the scaling-measurement preparation in a coherent states is illuminated. Furthermore, by exploiting the freedom in the parameter s, we introduce a computable and experimentally testable quantifier for optical nonclassicality, reveal its basic properties, and illustrate it by typical examples. A simple and convenient criterion for optical nonclassicality in terms of the 8-ordered phase-space distribution is derived.