We consider measurements with systems of on-off detectors. Quantum correlations will be directly revealed by higher order moments of the joint click counting statistics. Some applications to nonclassical states will be discussed.
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 photodetectors.
We address the problem of constructing witnesses for nonclassical light that are applicable in state-of-the-art photon-counting devices. The key ingredient for the criteria we derive are generalized and directly measurable counting statistics and matrices of counting moments. Beyond common criteria, we find classes of witnesses that are based on half-integer powers of click moments and counts. Remarkably, this leads to an exponential increase of the number of nonclassicality criteria one can construct and apply. With this finding, special attention is payed to probing even and odd parity states, requiring such distinct witnesses. Our method is applicable to spatial and time-bin multiplexing in optical systems, where each spatial and temporal mode can be measured with both on-off detectors and detectors with partial internal quasi-photon-number resolution. Generalizations to multimode scenarios are provided, allowing for the direct measurement of nonclassical correlations and coincidence counts between an arbitrary number of modes.