Reference-frame-independent measurement-device-independent quantum key distribution (RFI-MDI-QKD) can reduce the complexity of practical systems caused by the alignment of the reference frame. Lengthening the transmission distance and improving the system clock rate are essential in practical applications of QKD. Herein, in an asymptotic case, we report the results of RFI-MDI-QKD over a distance of 160 km at a clock rate of 50 MHz. By considering the statistical fluctuation of a finite key, we experimentally implemented a four-intensity decoy-state RFI-MDI-QKD protocol with biased bases at transmission distances of 100 km and 120 km. In addition, we compare the RFI-MDI-QKD protocol with the original MDI-QKD protocol when different misalignments of the reference frame are deployed. The results demonstrate the robustness of our scheme and that the key rate of RFI-MDI-QKD can be improved for a large misalignment of the reference frame.

中文翻译：

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基于极化复用的与测量设备无关的量子密钥分配，无需相位参考校准

与参考框架无关的与测量设备无关的量子密钥分配（RFI-MDI-QKD）可以降低由参考框架的对齐引起的实际系统的复杂性。在QKD的实际应用中，延长传输距离和提高系统时钟速率至关重要。在此，在渐近情况下，我们报告了在50 km的时钟速率下，在160 km的距离上RFI-MDI-QKD的结果。考虑到有限键的统计波动，我们在传输距离分别为100 km和120 km的情况下，通过实验实现了四强度诱饵状态的RFI-MDI-QKD协议。此外，当部署参考帧的不同对齐方式时，我们将RFI-MDI-QKD协议与原始MDI-QKD协议进行了比较。