Efficient quantification of non-Gaussian spin distributions

TL;DR

This paper presents a theoretical and experimental method for efficiently quantifying non-Gaussian spin distributions using cumulants, enabling unbiased, noise-resistant analysis suitable for quantum state detection in atomic ensembles.

Contribution

It introduces an unbiased cumulant-based approach for quantifying non-Gaussian states, optimized for realistic measurement conditions in atomic ensemble experiments.

Findings

Effective non-Gaussian quantification in cold Rb spin ensembles.

Unbiased estimators robust against measurement noise.

Application to quantum memory state analysis.

Abstract

We study theoretically and experimentally the quantification of non-Gaussian distributions via non-destructive measurements. Using the theory of cumulants, their unbiased estimators, and the uncertainties of these estimators, we describe a quantification which is simultaneously efficient, unbiased by measurement noise, and suitable for hypothesis tests, e.g., to detect non-classical states. The theory is applied to cold $^{87}$Rb spin ensembles prepared in non-gaussian states by optical pumping and measured by non-destructive Faraday rotation probing. We find an optimal use of measurement resources under realistic conditions, e.g., in atomic ensemble quantum memories.