Sub-Poissonian and anti-bunching criteria via majorization of statistics

TL;DR

This paper introduces a majorization-based method using confidence intervals to compare photon number uncertainties in quantum light states, offering a more comprehensive analysis than variance alone.

Contribution

It formulates majorization in terms of confidence intervals and applies it to analyze sub- and super-Posissonian behavior and bunching effects in various quantum states.

Findings

Majorization can reveal differences in photon statistics not captured by variance.

The method provides a more complete analysis of quantum light states.

Contradictions with variance-based predictions are demonstrated.

Abstract

We use majorization and confidence intervals as a convenient tool to compare the uncertainty in photon number for different quantum light states. To this end majorization is formulated in terms of confidence intervals. As a suitable case study we apply this tool to sub- and super-Posissonian behavior and bunching and anti- bunching effects. We focus on the most significant classical and nonclassical states, such as Glauber coherent, thermal, photon number, and squeezed states. We show that majorization provides a more complete analysis that in some relevant situations contradicts the predictions of variance.