We develop a theory and accompanying mathematical model for quantum communication via any number of intermediate entanglement-swapping operations and solve numerically for up to three intermediate entanglement-swapping operations. Our model yields two-photon interference visibilities postselected on photon counts at the intermediate entanglement-swapping stations. Realistic experimental conditions are accommodated through the parametric down-conversion rate, photon-counter efficiencies and dark-count rates, and instrument and transmission losses. We calculate achievable quantum communication distances such that two-photon interference visibility exceeds the Bell-inequality threshold.
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