Twin-field quantum key distribution with three mutually unbiased bases

Twin-field quantum key distribution (TF-QKD) and its variants provide a promising solution for sharing information-theoretic secure keys between intercity peers since they are able to overcome the fundamental rate-transmittance bound without quantum repeaters. In this paper, we propose to improve the key rate at long distances and the maximum achievable distance for TF-QKD by deriving the error rates under three mutually unbiased bases, i.e., aX, aY , and aZ in two-dimensional Hilbert space. Moreover, learning these error rates, one can add noisy preprocessing to further improve its performance. We also observe that higher bit error rates do not necessarily imply lower key rates when noisy preprocessing is added. Our method does not change the existing physical implementation or experimental operation, but only requires simple postprocessing of the experimental data, which can be directly used to improve the key rate performance of the existing QKD system. The simulation results demonstrate its notable enhancements in terms of key rate at long distances and the maximum achievable distance for the phase-encoded TF-QKD protocol.