Developing a practical model for noise in entangled-photon detection

We develop a comprehensive model for the effective two-photon density matrix produced by a parametric source of entangled-photon pairs under a variety of detector configurations commonly seen in a laboratory setting: two and four photon-number-resolving (PNR) and threshold detectors. We derive the probability of obtaining a single coincidence assuming Poisson-distributed photon pairs, nonunit detection efficiency, and dark counts; obtain the effective density matrix; and use this quantity to compute the fidelity of this state with respect to the maximally entangled ideal. The four-detector PNR case admits an analytic result valid for any combination of parameters, while all other cases leverage low-efficiency approximations to arrive at closed-form expressions. Interestingly, our model reveals appreciable fidelity improvements from four detectors as opposed to two but minimal advantages for PNR over threshold detectors in the regimes explored. Overall, our work provides a valuable tool for the quantitative design of two-photon experiments under realistic nonidealities.