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Physica Scripta

Effect of weak randomness on practical reference-frame-independent measurement-device-independent quantum key distribution

Jian-Rong Zhu, Chuan-Hao Shu, Yuhang Zhao, Xiao-Ming Lu, Chun-Mei Zhang, Hong-Wei Li

Published Mar 17, 2026• 0 citations
Publisher

Abstract

Abstract Reference-frame-independent measurement-device-independent quantum key distribution (RFI-MDI-QKD) is considered one of the most promising protocols, as it can generate secret keys without reference frame alignment and defeat all attacks on the measurement side. A fundamental assumption for the security of RFI-MDI-QKD is that both senders can prepare their quantum states with perfect randomness. However, in practical implementations, this assumption may be violated, primarily due to limitations in the imperfect random numbers and quantum device imperfections. In this work, we investigate the effect of weak randomness on the state preparation in practical decoy-state RFI-MDI-QKD, demonstrating that even a small proportion of weak randomness severely compromises the security of RFI-MDI-QKD. Furthermore, we apply the advantage distillation (AD) method to counteract the performance degradation caused by weak randomness in RFI-MDI-QKD. Simulation results demonstrate that AD can significantly improve both the secret key rate and the maximum transmission distance for practical decoy-state RFI-MDI-QKD under weak randomness conditions. These results represent a critical advance toward the development of secure, long-distance, multi-node quantum communication networks.

DOI
10.1088/1402-4896/ae535f

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Abstract Reference-frame-independent measurement-device-independent quantum key distribution (RFI-MDI-QKD) is considered one of the most promising protocols, as it can generate secret keys without reference frame alignment and defeat all attacks on the measurement side. A fundamental assumption for the security of RFI-MDI-QKD is that both senders can prepare their quantum states with perfect randomness. However, in practical implementations, this assumption may be violated, primarily due to limitations in the imperfect random numbers and quantum device imperfections. In this work, we investigate the effect of weak randomness on the state preparation in practical decoy-state RFI-MDI-QKD, demonstrating that even a small proportion of weak randomness severely compromises the security of RFI-MDI-QKD. Furthermore, we apply the advantage distillation (AD) method to counteract the performance degradation caused by weak randomness in RFI-MDI-QKD. Simulation results demonstrate that AD can significantly improve both the secret key rate and the maximum transmission distance for practical decoy-state RFI-MDI-QKD under weak randomness conditions. These results represent a critical advance toward the development of secure, long-distance, multi-node quantum communication networks.
Perfect randomness is of great significance in various quantum key distribution (QKD) protocols. In this Letter, we investigate the effect of weak randomness on the state preparation in reference-frame-independent QKD (RFI-QKD), which may be implemented with imperfect random numbers or quantum-state encoding devices. In the scenario of weak randomness, the maximal amount of information the eavesdropper can acquire should be carefully evaluated. With practical experimental parameters, we demonstrate that even a small proportion of weak randomness will impact the security of RFI-QKD seriously. Furthermore, we briefly study the side effect of weak randomness on RFI measurement-device-independent QKD (RFI-MDI-QKD), and simulation results show that weak randomness damages the performance of RFI-MDI-QKD more critically than that of RFI-QKD.
The reference-frame-independent quantum key distribution (RFI-QKD) has the advantage of tolerating reference frames that slowly vary. It can generate secure keys between two remote users with slowly drifted and unknown reference frames. However, the drift of reference frames may inevitably compromise the performance of QKD systems. In the paper, we employ the advantage distillation technology (ADT) to the RFI-QKD and the RFI measurement-device-independent QKD (RFI MDI-QKD), and we then analyze the effect of ADT on the performance of decoy-state RFI-QKD and RFI MDI-QKD in both asymptotic and nonasymptotic cases. The simulation results show that ADT can significantly improve the maximum transmission distance and the maximum tolerable background error rate. Furthermore, the performance of RFI-QKD and RFI MDI-QKD in terms of the secret key rate and maximum transmission distance are still greatly improved when statistical fluctuations are taken into account. Our work combines the merits of the ADT and RFI-QKD protocols, which further enhances the robustness and practicability of QKD systems.
Abstract Reference-frame-independent measurement-device-independent quantum key distribution (RFI-MDI-QKD) can remove all potential detector side-channel attacks and the requirement of real-time alignment of reference frames. However, all previous RFI-MDI-QKD implementations assume the perfect state preparation in sources, which is impractical and may lead to security loopholes. Here, we propose an RFI-MDI-QKD protocol which is robust against state preparation flaws. Comparing to the conventional six-state RFI-MDI-QKD, our scheme can be realized with only four flawed states, which improves the practical security of RFI-MDI-QKD and simplifies the experimental implementation. In addition, simulation results demonstrate that source flaws in Z basis have adverse effect on the performance of RFI-MDI-QKD while the source flaws in X and Y bases have almost no effect. We hope that this work could provide a valuable reference for practical implementations of RFI-MDI-QKD.
Reference-frame-independent measurement-device-independent quantum key distribution (RFI-MDI-QKD) is a novel protocol that eliminates all possible attacks on the detector side and the necessity of reference-frame alignment in source sides. However, its performance may degrade notably due to statistical fluctuations since more parameters, e.g., yields and error rates for mismatched-basis events, must be accumulated to monitor the security. In this work, we find that the original decoy states method estimates these yields overpessimistically since it ignores the potential relations between different bases. Through jointly processing parameters of different bases, the performance of RFI-MDI-QKD is greatly improved in terms of the secret key rate and achievable distance when statistical fluctuations are considered (the statistical fluctuation analysis is the first step to the final analysis of the finite key size effect). Our results pave an avenue towards practical RFI-MDI-QKD.
Advantage distillation (AD) provides a means of separating highly correlated raw key bits from weakly correlated information in quantum key distribution (QKD). In this Letter, we apply the AD method to improve the performance of reference-frame-independent QKD (RFI-QKD). Simulation results show that, compared with RFI-QKD without AD, RFI-QKD with AD can tolerate higher system errors and obtain better performance on the secret key rate and transmission distance. Furthermore, we extend the AD method to RFI measurement-device-independent QKD (RFI-MDI-QKD) and demonstrate that the AD method can improve the performance of RFI-MDI-QKD more significantly.
Quantum cryptography has a strong security that classical cryptography cannot match, and quantum key distribution (QKD) is the most important method of quantum cryptography. Reference-frame-independent measurement-device-independent QKD (RFI-MDI-QKD) protocol can avoid the drift of the reference frame and all side channels of measurement devices. However, RFI MDI-QKD usually employs a weak coherent state (WCS) as the light source, which limits the transmission distance of secure keys. Here, by using heralded single-photon sources, we investigate an improved decoy-state RFI-MDI-QKD scheme. We perform numerical simulations for the scheme under different scenarios, such as considering the finite size and different drift angles. Compared with the scheme with WCS, our scheme can significantly improve the transmission distance of RFI-MDI-QKD.