Security research on practical measurement-device-independent quantum key distribution

The ideal measurement-device-independent quantum key distribution (MDI-QKD), which is immune to all detector side-channel attacks, is built on the Bell state measurement of two single-photon states. However, in practical MDI-QKD where phase-randomized weak coherent pulses (PR-WCPs) are used, the mismatch between states preparation and measurement in X basis leads to the bit error rate of more than 25%, which poses a challenge to the security of QKD. In this paper, we provide a security analysis of practical MDI-QKD based on polarization coding. We analyze the Hong-Ou-Mandel interference of PR-WCPs and Poisson-distributed photon number states (PNs), and find that these two sources are equivalent in MDI-QKD. The security analysis based on entanglement distillation is carried out on PNs, and the measurement results in Z basis and X basis are averaged to overcome the noncorrelation of the error rates in these two bases. Compared with GLLP scheme, a tighter key rate is obtained in this work, and the key rate deviates from the linear key rate bound in a short distance due to the finite proportion of multiphoton terms.

Figure 1

Schematic diagram of MDI-QKD.

Figure 2

Comparison of the HOM interference for single-photon source, Poisson distributed PNs and PR-WCPs.

Figure 3

Comparison of BER and PER in (a) Z basis and (b) X basis. In this figure, the average photon number $\mu$ is set to 0.3 when the communication distance is 0 km.

Figure 4

Gain comparison between Z basis (blue curves) and X basis (red curves) for $\mu =0.2$ and $\mu =0.5$ in logarithmic coordinate.

Figure 5

(a) Dependence of key rate on the average photon number $\mu$, (b) Key rate comparison for MDI-QKD between this work and that obtained by GLLP scheme with decoy state method [43].