to wit: "We will also frequently make reference to the set of coherent states which we denote by $\{|\alpha\rangle\}$...It is known that every quantum state of light ρ permits a representation that is diagonal with respect to coherent states, i.e.
$$\rho = \int d^2\alpha\,P(\alpha)|\alpha\rangle \langle \alpha |$$ where the coefficient $P(\alpha)$ is called the Glauber-Sudarshan P distribution. The P distribution always sums to 1 but may display negativities, in which case it is considered nonclassical. On the other hand, P distributions that exhibit the properties of a classical, nonnega…