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Estimation of P1
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High-efficiency single-photon generation via large-scale active time multiplexing

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We estimated a single-photon probability P1, assuming that the probability of more than two photons is negligibly small; a multiplexed k-photon probability Pk for k ≥ 3 is expected <1.5% of P1 for μ = 0.18 in our experiment. We modeled our SPDs as bucket detectors that discriminate between zero and one or more photons. The NPBS’s transmission/reflection ratio is also assumed to be 1. With those assumptions, single and coincidence count rates are given by$Si=P1Rη2+P2R{η2+η(2−η)4}$(4)$C=P2Rη22$(5)where P2 is the probability of a two-photon state after multiplexing. The second and third terms in Eq. 4 are the respective detector click probabilities that one and two of two photons arrive at detector i. Equation 2 is obtained by substituting Eq. 5 into Eq. 4.

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