Quantum key distribution with two-segment quantum repeaters

Quantum repeaters represent one possible way to achieve long-distance quantum key distribution. One way of improving the repeater rate and decreasing the memory coherence time is the usage of multiplexing. Motivated by the experimental fact that long-range connections are practically demanding, we extend the analysis of the quantum repeater multiplexing protocol to the case of short-range connections. We derive formulas for the repeater rate and we show that short-range connections lead to most of the benefits of a full-range multiplexing protocol. A less demanding QKD-protocol without quantum memories was recently introduced by Lo et al. We generalize this measurement-device-independent quantum key Distribution protocol to the scenario where the repeater Station contains also heralded quantum memories. We assume either single-photon sources or weak coherent pulse sources plus decay states. We show that it is possible to significantly outperform the original proposal, even in presence of decoherence of the quantum memory. We give formulas in terms of device imperfections i.e., the quantum bit error rate and the repeater rate.