title: 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 photodetectors.
authors: Arbeitsgruppe Theoretische Quantenoptik, Institut für Physik, Universität Rostock, D-18051 Rostock, Germany.|Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom.
authors: J
authors: J
authors: Sperling
authors: Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom.|Universität Paderborn, Warburger Strasse 100, 33098 Paderborn, Germany.
authors: T J
authors: TJ
authors: Bartley
authors: Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom.
authors: G
authors: G
authors: Donati
authors: Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom.|Dipartimento di Scienze, Università degli Studi Roma Tre, Via della Vasca Navale 84, 00146 Rome, Italy.
authors: M
authors: M
authors: Barbieri
authors: Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom.|State Key Laboratory of Advanced Optical Communication Systems and Networks, Institute of Natural Sciences & Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China.
authors: X-M
authors: XM
authors: Jin
authors: Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom.
authors: A
authors: A
authors: Datta
authors: Arbeitsgruppe Theoretische Quantenoptik, Institut für Physik, Universität Rostock, D-18051 Rostock, Germany.
authors: W
authors: W
authors: Vogel
authors: Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom.
authors: I A
authors: IA
authors: Walmsley