Improving device-independent quantum key distribution protocols through multiple routed Bell tests
Device-independent quantum key distribution (DI-QKD) offers security with the smallest possible set of assumptions about the experimental setup. The challenge posed by its implementation could be tackled using routed Bell tests with entanglement swapping, or distant Bell state measurement (BSM) units. However, practical distances still require local tests with close-to-ideal violations. We propose a DI-QKD protocol based on multiple sources and measurement devices where, in each round, routed tests are performed on randomly selected local devices. The violation of local Bell tests is checked even when a successful BSM projection is achieved. By requiring that such conditional tests remain consistent with the overall one, we achieve improvements in the critical detection efficiencies of about $4-12\%$ for high visibilities. Our approach enables long-distance DI-QKD, with access to highly efficient loophole-free routing setups, and multiple local tests (possibly imperfect) with very high local detection efficiencies. Finally, we extend the concept of routing to dimension witnesses, where qubit-bounded sources send states to the BSM. This can be seen as a semi-device-independent extension of the aforementioned protocol.