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

We develop a theory for long-distance quantum key distribution based on concatenated entanglement swapping using parametric down-conversion sources and show numerical results of our model. The model incorporates practical resources including multi-pair sources, inefficient detectors with dark counts and lossy channels. We calculate the maximum secret key-generation ratefor up to three entanglement swapping stations by optimizing over resource parameters, and 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 approach the Takeoka-Guha-Wilde upper bound. Our analysis demonstrates the need for new technology such as quantum memory to synchronize photons and our methods should serve as a valuable component for accurately modelling quantum-memory-based long-distance quantum key distribution.