  In entanglement-based quantum key distribution (QKD), the generation and
detection of multi-photon modes leads to a trade-off between entanglement
visibility and two-fold coincidence events when maximizing the secure key rate
(SKR). We produce a predictive model for the optimal two-fold coincidence
probability per coincidence window given the channel efficiency and detector
dark count rate of a given system. This model is experimentally validated and
used in simulations for QKD with satellites as well as optical fibers.
