Husimi Q representation
The Husimi Q representation, introduced by Kôdi Husimi in 1940, is a quasiprobability distribution commonly used in quantum mechanics to represent the phase space distribution of a quantum state such as light in the phase space formulation. It is used in the field of quantum optics and particularly for tomographic purposes. It is also applied in the study of quantum effects in superconductors.
The Husimi Q distribution (called Q-function in the context of quantum optics) is one of the simplest distributions of quasiprobability in phase space. It is constructed in such a way that observables written in anti-normal order follow the optical equivalence theorem. This means that it is essentially the density matrix put into normal order. This makes it relatively easy to calculate compared to other quasiprobability distributions through the formula
which is effectively a trace of the density matrix over the basis of coherent states . It produces a pictorial representation of the state ρ to illustrate several of its mathematical properties. Its relative ease of calculation is related to its smoothness compared to other quasiprobability distributions. In fact, it can be understood as the Weierstrass transform of the Wigner quasiprobability distribution, i.e. a smoothing by a Gaussian filter,
...
Wikipedia