Detector imperfections in photon-pair source characterization

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We analyze how imperfections in single-photon detectors impact the characterization of photon-pair sources. We perform exact calculations to reveal the effects of multi-pair emissions and of noisy, non-unit efficiency, non photon-number resolving detections on the Cauchy-Schwarz parameter, on the second order auto-correlation and cross-correlation functions, and on the visibilities of both Hong-Ou-Mandel and Bell-like interferences. We consider sources producing either two-mode squeezed states or states with a Poissonian photon distribution. The proposed formulas are useful in practice to determine the impacts of multi-pair emissions and dark counts in standard tests used in quantum optics.