Tight inequalities for nonclassicality of measurement statistics

TL;DR

This paper derives tight inequalities that precisely characterize nonclassical measurement statistics in quantum optics, enabling experimental verification of nonclassicality with minimal resources.

Contribution

It provides a necessary and sufficient set of inequalities for identifying nonclassical measurement statistics, including analytical forms for key measurement scenarios.

Findings

Derived tight inequalities for classical and nonclassical statistics

Identified nonclassical properties of phase-squeezed coherent states

Demonstrated experimental verification with minimal resources

Abstract

In quantum optics, measurement statistics -- for example, photocounting statistics -- are considered nonclassical if they cannot be reproduced with statistical mixtures of classical radiation fields. We have formulated a necessary and sufficient condition for such nonclassicality. This condition is given by a set of inequalities that tightly bound the convex set of probabilities associated with classical electromagnetic radiation. Analytical forms for full sets and subsets of these inequalities are obtained for important cases of realistic photocounting measurements and unbalanced homodyne detection. As an example, we consider photocounting statistics of phase-squeezed coherent states. Contrary to a common intuition, the analysis developed here reveals distinct nonclassical properties of these statistics that can be experimentally corroborated with minimal resources.