Revealing nonclassicality via s-ordered phase-space distribution

Nonclassical states play a crucial role in both theoretical and experimental investigations of quantum optics, and there is a wide interest in characterization and quantification of nonclassicality. By exploiting the freedom of the parameter s in the s-ordered phase-space distribution introduced by Cahill and Glauber [Phys. Rev. 177, 1882 (1969)], we develop a method to reveal and quantify optical nonclassicality via the divided difference of the s-ordered phase-space distribution. Our approach yields naturally a family of quantifiers of optical nonclassicality, which have many desirable properties such as convexity and monotonicity under the Gaussian noise channels. The quantifiers are illustrated by evaluating nonclassicality of several typical states. Two simple and convenient criteria for nonclassicality are established, which in particular certify all nonclassical Gaussian states.