Photon distributions and information nonnegativity versus quadrature uncertainty relation

TL;DR

This paper derives new inequalities for classical polynomials using entropic inequalities for Shannon entropies and explores how photon distribution functions relate to quadrature uncertainty violations in quantum states.

Contribution

It introduces novel inequalities for classical polynomials based on entropic inequalities and analyzes their connection to quantum state properties.

Findings

Photon distribution functions are expressed in terms of classical polynomials.

Violations of quadrature uncertainty relate to the sign and existence of distribution functions.

New inequalities for Hermite, Laguerre, Legendre polynomials are established.

Abstract

Using entropic inequalities for Shannon entropies new inequalities for some classical polynomials are obtained. To this end, photon distribution functions for one-, two- and multi-mode squeezed states in terms of Hermite, Laguerre, Legendre polynomials and Gauss' hypergeometric functions are used. The dependence between the violation of the quadrature uncertainty relation, the sign and the existence of the distribution function of such states is considered.