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We develop a theory for long-distance quantum key distribution based onconcatenated entanglement swapping using parametric down-conversion sources andshow numerical results of our model. The model incorporates practical resourcesincluding multi-pair sources, inefficient detectors with dark counts and lossychannels. We calculate the maximum secret key-generation ratefor up to threeentanglement swapping stations by optimizing over resource parameters, and ournumerical simulation shows that the range of quantum key distribution can inprinciple be markedly increased but at the expense of an atrociously unfeasiblesecret key-generation rate; however, the upper bound of our key rates closelyapproach the Takeoka-Guha-Wilde upper bound. Our analysis demonstrates the needfor new technology such as quantum memory to synchronize photons and ourmethods should serve as a valuable component for accurately modellingquantum-memory-based long-distance quantum key distribution.

Practical long-distance quantum key distribution through concatenated entanglement swapping with parametric down-conversion sources