Classical and quantum-mechanical phase space distributions

TL;DR

This paper investigates the classicality of phase space distributions in quantum optics, showing that only specific quasiprobabilities align with classical electrodynamics principles, thereby refining the definition of nonclassicality.

Contribution

It demonstrates that s-parameterized quasiprobabilities uniquely describe classical superposition, and that the P function is the only quantum quasiprobability transforming classically under attenuation.

Findings

s-parameterized quasiprobabilities describe classical superposition

Glauber-Sudarshan P function transforms classically under attenuation

Strengthens the P function's role in defining nonclassicality

Abstract

We examine the notion of nonclassicality in terms of quasiprobability distributions. In particular, we do not only ask if a specific quasiprobability can be interpreted as a classical probability density, but require that characteristic features of classical electrodynamics are resembled. We show that the only quasiprobabilities which correctly describe the superposition principle of classical electromagnetic fields are the $s$-parameterized quasiprobabilities. Furthermore, the Glauber-Sudarshan P function is the only quantum-mechanical quasiprobability which is transformed at a classical attenuator in the same way as a classical probability distribution. This result strengthens the definition of nonclassicality in terms of the P function, in contrast to possible definitions in terms of other quasiprobabilities.