Quantum Correlations from the Conditional Statistics of Incomplete Data

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.

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Cited by in corpus (14)

• Incomplete Detection of Nonclassical Phase-Space Distributions
• Conditional Hybrid Nonclassicality
• Detector-Independent Verification of Quantum Light
• Direct calibration of click-counting detectors
• Measuring coherence of quantum measurements
• Neural-network approach for identifying nonclassicality from click-counting data
• Geometrical picture of photocounting measurements
• Identification of nonclassical properties of light with multiplexing layouts
• Quantum correlations in composite systems
• General modeling framework for quantum photodetectors
• Detection-device-independent verification of nonclassical light
• Witnessing non-classicality through large deviations in quantum optics
• Detector entanglement: Quasidistributions for Bell-state measurements
• Continuity of measurement outcomes