Nonclassicality and the concept of local constraints on the photon number distribution

TL;DR

This paper uses classical moment problem techniques to analyze photon number distributions, revealing local constraints that distinguish classical from nonclassical states and challenging the idea that oscillations indicate nonclassicality.

Contribution

It introduces a novel application of the Stieltjes moment problem to derive local classicality constraints on photon number distributions.

Findings

Photon number distributions follow moment constraints from the classical moment problem.

Local constraints on p_n can identify nonclassical states.

Oscillations in p_n are not necessarily signatures of nonclassicality.

Abstract

We exploit results from the classical Stieltjes moment problem to bring out the totality of all the information regarding phase insensitive nonclassicality of a state as captured by the photon number distribution p_n. Central to our approach is the realization that n !p_n constitutes the sequence of moments of a (quasi) probability distribution, notwithstanding the fact that p_n can by itself be regarded as a probability distribution. This leads to classicality restrictions on p_n that are local in n involving p_n's for only a small number of consecutive n's, enabling a critical examination of the conjecture that oscillation in p_n is a signature of nonclassicality.