Quantum Correlations from the Conditional Statistics of Incomplete Data

TL;DR

This paper investigates quantum correlations in light fields using click-counting detectors with incomplete data, establishing criteria to identify nonclassical correlations without assumptions on detector imperfections.

Contribution

It introduces new nonclassicality criteria based on conditional and joint click statistics that do not rely on detector response assumptions.

Findings

Demonstrated nonclassical correlations in parametric down conversion light.

Verified quantum correlations in heralded single-photon states.

Criteria successfully distinguish joint and conditional quantum correlations.

Abstract

We study, in theory and experiment, the quantum properties of correlated light fields measured with click-counting detectors providing incomplete information on the photon statistics. We establish a correlation parameter for the conditional statistics, and we derive the corresponding nonclassicality criteria for detecting conditional quantum correlations. Classical bounds for Pearson's correlation parameter are formulated that allow us, once they are violated, to determine nonclassical correlations via the joint statistics. On the one hand, we demonstrate nonclassical correlations in terms of the joint click statistics of light produced by a parametric down conversion source. On the other hand, we verify quantum correlations of a heralded, split single-photon state via the conditional click statistics together with a generalization to higher-order moments. We discuss the performance of the presented nonclassicality criteria to successfully discern joint and conditional quantum correlations. Remarkably, our results are obtained without making any assumptions on the response function, quantum efficiency, and dark-count rate of the photodetectors.