Glauber-Sudarshan representation ($\rho =\int P(\alpha )|\alpha ⟩⟨\alpha |d^2\alpha$)

The diagonal coherent state representation writes a single-mode density matrix in the form shown. Its weight may be a generalized distribution rather than an ordinary nonnegative probability density. A nonclassical state of light has no nonnegative measure of this form. This use of $P$ differs from the Wigner distribution; a nonnegative Wigner function does not by itself certify classicality.