Asymmetric sending or not sending twin-field quantum key distribution in practice

Quantum key distribution (QKD) offers a secret way to share keys between legitimate users which is guaranteed by the law of quantum mechanics. Most recently, the limitation of transmission distance without quantum repeaters was broken through by twin-field QKD [M. Lucamarini et al., Nature (London) 557, 400 (2018)]. Based on its main idea, sending or not-sending (SNS) QKD protocol was proposed [X. B. Wang et al. Phys. Rev. A 98, 062323 (2018)], which filled the remaining security loopholes and can tolerate large misalignment errors. In this paper, we give a more general model for SNS QKD, where two legitimate users, Alice and Bob, can possess asymmetric quantum channels. By applying the method present in the paper, the legitimate users can achieve dramatically increased key generation rates and transmission distances compared with compensating the channel asymmetry and utilizing the original symmetric protocol. Therefore, our present paper represents a further step along the progress of practical QKD.

Figure 1

Schematic setup of asymmetric SNS TF-QKD. WCS: Weak coherent source. PM: phase modulator; IM: intensity modulator; D1(D2): single-photon detector. Bob is farther from UTP than Alice; $L_a$ and $L_b$ are the distance between the user and the UTP, respectively.

Figure 2

Result of secret key rates with respect to the total transmission distance ($L_a+L_b$). The line marked with $Sym$ represents the symmetric case; $L_a=0$ represents the extreme case that Alice and UPT are located in the same position. The rest lines correspond to asymmetric cases: Label $N\_asy$ refers to utilizing the asymmetric method in this paper; $O\_asy$ is for directly using the original treating method by adding extra attenuations; the numbers in the label denote the value of $L_b-L_a$. PLOB bound and single-repeater bound represent theoretical bounds from Refs. [10, 27].

Figure 3

Comparison of key rates between single-arm SNS TF-QKD ($\mathrm{S}\_\mathrm{SNS}$) and four-intensity decoy-state BB84 under different misalignment errors (0.05, 0.075, and 0.1). PLOB bound is also plotted.

Figure 4

Variations of the secret key rate with the changing of the misalignment error $E_d$ when $L_a=50\mathrm{km}, L_b=150\mathrm{km}$.