Wigner Quasiprobability Distribution - Other Related Quasiprobability Distributions

Other Related Quasiprobability Distributions

The Wigner distribution was the first quasiprobability distribution to be formulated, but many more followed, formally equivalent and transformable to and from it (viz. Transformation between distributions in time–frequency analysis). As in the case of coordinate systems, on account of varying properties, several such have with various advantages for specific applications:

• Glauber P representation
• Husimi Q representation

Nevertheless, in some sense, the Wigner distribution holds a privileged position among all these distributions, since it is the only one whose requisite star product drops out (integrates out by parts to effective unity) in the evaluation of expectation values, as illustrated above, and so can be visualized as a quasiprobability measure analogous to the classical ones.