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We develop a theory for long-distance quantum key distribution based on concatenated entanglement swapping using parametric down-conversion sources and show the numerical results of our model. The model incorporates practical resources including multipair sources, inefficient detectors with dark counts, and lossy channels. We calculate the maximum secret key-generation rate for up to three entanglement swapping stations by optimizing resource parameters. Our numerical simulation shows that the range of quantum key distribution can, in principle, be markedly increased but at the expense of an atrociously unfeasible secret key-generation rate; however, the upper bound of our key rates closely approaches the Takeoka–Guha–Wilde upper bound. Our analysis demonstrates the need for new technology, such as quantum memory, to synchronize photons; our methods should serve as a valuable component for accurately modeling quantum-memory-based long-distance quantum key distribution.
© 2015 Optical Society of America
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