Efficient Quantification of Non-Gaussian Spin Distributions

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 nonclassical states. The theory is applied to cold Rb-87 spin ensembles prepared in non-Gaussian states by optical pumping and measured by nondestructive Faraday rotation probing. We find an optimal use of measurement resources under realistic conditions, e. g., in atomic ensemble quantum memories.