Security Analysis of Sending or Not-Sending Twin-Field Quantum Key Distribution with Weak Randomness

Abstract

Sending-or-not sending twin-field quantum key distribution (SNS TF-QKD) has the advantage of tolerating large amounts of misalignment errors, and its key rate can exceed the linear bound of repeaterless quantum key distribution. However, the weak randomness in a practical QKD system may lower the secret key rate and limit its achievable communication distance, thus compromising its performance. In this paper, we analyze the effects of the weak randomness on the SNS TF-QKD. The numerical simulation shows that SNS TF-QKD can still have an excellent performance under the weak random condition: the secret key rate can exceed the PLOB boundary and achieve long transmission distances. Furthermore, our simulation results also show that SNS TF-QKD is more robust to the weak randomness loopholes than the BB84 protocol and the measurement-device-independent QKD (MDI-QKD). Our results emphasize that keeping the randomness of the states is significant to the protection of state preparation devices.

Keywords: asymptotic cases; finite-key; twin-field quantum key distribution; weak randomness.

Figure 1

(Color online) The optimal key rate (bits per pulse) in logarithmic scale versus transmission distance between Alice and Bob when the weak randomness exists for only one party (Alice or Bob) $p_1={10}^{-x}(x=6,5,4,3),p_2=0$(curves from right to left). The dashed lines are results of the asymptotic case, and the solid lines are the results of the finite-key size $N={10}^{15}$. The gray dotted line is the PLOB bound.

Figure 2

(Color online)The optimal key rate (bits per pulse) in logarithmic scale versus transmission distance between Alice and Bob when the weak randomness exists for two parties $p_1=p_2={10}^{-x}(x=6,5,4,3)$(curves from right to left). The dashed lines are results of asymptotic cases and the solid lines are the results of the finite-key size $N={10}^{15}$. The gray dotted line is the PLOB bound.

Figure 3

(Color online)The optimal key rate (bits per pulse) in logarithmic scale versus transmission distance between Alice and Bob with weak randomness $p_1=p_2={10}^{-6}$ and without weak randomness $p_1=p_2=0$ for different $N={10}^x(x=12,13,15)$ (curves from left to right), the dashed lines are results of weak randomness for different N, and the solid lines are the results of non-weak randomness for different N. The gray dotted line is the PLOB bound.

Figure 4

(Color online) The optimal key rate (bits per pulse) in logarithmic scale versus transmission distance between Alice and Bob with weak randomness $p_1=p_2=0,{10}^{-x}(x=6,5,4,3)$ (curves from right to left) for different $N={10}^{13}$, $N={10}^{15}$, the dashed lines are results $N={10}^{13}$ with different weak randomness parameters, and the solid lines are the results of $N={10}^{15}$ with different weak randomness parameters. The gray dotted line is the PLOB bound.

Figure 5

(Color online)The optimal key rate (bits per pulse) in logarithmic scale versus transmission distance between Alice and Bob with weak randomness in the BB84 protocol, the MDI-QKD and the SNS TF-QKD. The blue lines are results weak randomness parameters, and the solid lines are the results of $N={10}^{15}$ with different weak randomness parameters.