Improving the performance of twin-field quantum key distribution

Among the various versions of the twin-field quantum key distribution (TF-QKD) protocol [M. Lucamarini, Z. Yuan, J. Dynes, and A. Shields, Nature (London) 557, 400 (2018)] that can overcome the rate-distance limit, the TF-QKD without phase postselection proposed by Cui et al. [Phys. Rev. Appl. 11, 034053 (2019)] is an elegant TF-QKD that can provide high key rates since the postselection of global phases has been removed. However, the achievable distance of this variant is shorter than that of the original phase-matching QKD [X. Ma, P. Zeng, and H. Zhou, Phys. Rev. X 8, 031043 (2018)]. In this paper, we propose a method for improving its performance by introducing an additional decoy mode. The upper bound of the information leakage can be more tightly estimated; hence, both the key rate and the achievable distance are significantly improved. Interestingly, the operation of the proposed additional decoy mode is the same as that of the code mode; hence, it does not introduce difficulties into the experimental system. In addition, the improvement is substantial with finite decoy states, which is meaningful in practice.

Figure 1

Secret key rates in logarithmic scale as functions of the distance for various protocols with infinite decoy states. The blue solid line and red dashed-dotted line correspond to, respectively, our improved method and the original NPP-TFQKD. The purple dashed line corresponds to PM-QKD. The yellow dotted line corresponds to the repeaterless bound that was proposed in Ref. [12]; here, we refer to it as the linear bound.

Figure 2

Secret key rates in logarithmic scale as functions of the distance for various practical protocols. The blue solid line corresponds to our improved method with five-intensity decoy mode 1 and four-intensity decoy mode 2. The red dashed-dotted line corresponds to the original NPP-TFQKD with four decoy states. The yellow dotted line represents the linear bound that was proposed in Ref. [12]. The original NPP-TFQKD requires only the code mode and decoy mode. The intensity $\mu$ (the first decoy state and the code state) is an optimized value. Other decoy intensities, namely, ${\nu }_1$, ${\nu }_2$, and $o$, are fixed to 0.005, 0.002, and 0, respectively. For our improved protocol, the intensity $\mu$ is an optimized value. ${\nu }_1$, ${\nu }_2$, and $o$ are set to the same values as above. The additional intensity ${\mu }_3$ of decoy mode 1 is fixed to 1.3.