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arXiv:2601.04949

High-Rate Free-Running Reference-Frame-Independent Measurement-Device-Independent Quantum Key Distribution with Classified Distillation

Xin Liu, Zhicheng Luo, Kaibiao Qin, Jiawang Liu, Zhenrong Zhang, Kejin Wei

quant-phSubmitted Jan 8, 2026• Announced Jan 9, 2026• 0 citations
arXivHTMLPDF

Abstract

Reference-frame-independent measurement-device-independent quantum key distribution (RFI-MDI-QKD) eliminates detector side-channel attacks and avoids reference-frame calibration. While its feasibility has been widely demonstrated, existing implementations typically assume fixed or slowly drifting reference-frame misalignment, conditions rarely satisfied outside the laboratory. In realistic environments, rapid and free-running reference-frame variations can severely degrade both the key rate and transmission distance of conventional RFI-MDI-QKD. Here we propose a free-running RFI-MDI-QKD protocol that maintains high-rate key generation under rapid reference-frame variations. By introducing a classification-distillation method that reclassifies total detection events, secure keys can be extracted without modifying the experimental setup. Our protocol achieves a key rate more than nine times higher than the best previous RFI-MDI-QKD scheme and tolerates channel losses exceeding 24 dB, where earlier approaches fail. These results enable practical quantum key distribution on mobile platforms, including satellite-to-ground links and airborne nodes.

Comments
5 pages, 4 figures

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Reference-frame-independent measurement-device-independent quantum key distribution (RFI-MDI-QKD) eliminates detector side-channel attacks and avoids reference-frame calibration. While its feasibility has been widely demonstrated, existing implementations typically assume fixed or slowly drifting reference-frame misalignment, conditions rarely satisfied outside the laboratory. In realistic environments, rapid and free-running reference-frame variations can severely degrade both the key rate and transmission distance of conventional RFI-MDI-QKD. Here we propose a free-running RFI-MDI-QKD protocol that maintains high-rate key generation under rapid reference-frame variations. By introducing a classification-distillation method that reclassifies total detection events, secure keys can be extracted without modifying the experimental setup. Our protocol achieves a key rate more than nine times higher than the best previous RFI-MDI-QKD scheme and tolerates channel losses exceeding 24 dB, where earlier approaches fail. These results enable practical quantum key distribution on mobile platforms, including satellite-to-ground links and airborne nodes.
Abstract Rapidly and randomly drifted reference frames will shorten the transmission distance and decrease the secure key rate of realistic quantum key distribution (QKD) systems. In this article, we present a free-running reference-frame-independent (RFI) QKD scheme, where measurement events are classified into multiple slices with similar estimated classification parameter. We perform the free-running RFI QKD experiment with a fiber link of 100 km and reference frame misalignment more than 29 periods in 50.7 h. A key rate as high as 742.98 bps is achieved at the total loss of 31.5 dB benefiting from both the new protocol design and the 80 MHz repetition rate system in use. Our system runs 50.7 h freely without any reference frame alignment. In the experiment, the misalignment variation rate tolerance of the experiment is 0.262 rad/s, and could be optimized to 1.309 rad/s. Therefore, our free-running RFI scheme can be efficiently adapted into the satellite-to-ground and drone-based mobile communication scenarios.
Among all present quantum key distribution protocols, the reference-frame-independent measurement-device-independent quantum key distribution (RFI-MDI-QKD) is standing out due to its high security and practicability, since it can not only remove all detector-side-channel attacks, but also relax the requirement of reference-frame calibrations. However, till today, the performance degradation of RFI-MDI-QKD caused by finite-size effects is one of the biggest impediment to its practical implementations. Here, we propose an enhanced RFI-MDI-QKD protocol which is highly resistant to the finite-size effect and immensely boosts both the key rate and transmission distance. As a result, it can even surpass the most advanced MDI-QKD protocol under larger rotation angles of reference frames. Furthermore, with the state-of-the-art RFI-MDI-QKD setup, we successfully carry out a proof-of-principle experimental demonstration at a record distance of 300km. The experiments under non-ideal condition verify the advantage and robustness of our present work.
Measurement-device-independent quantum key distribution (MDI-QKD) is proved to be able to eliminate all potential detector side channel attacks. Combining with the reference frame independent (RFI) scheme, the complexity of practical system can be reduced because of the unnecessary alignment for reference frame. Here, based on polarization multiplexing, we propose a time-bin encoding structure, and experimentally demonstrate the RFI-MDI-QKD protocol. Thanks to this, two of the four Bell states can be distinguished, whereas only one is used to generate the secure key in previous RFI-MDI-QKD experiments. As far as we know, this is the first demonstration for RFI-MDI-QKD protocol with clock rate of 50 MHz and distance of more than hundred kilometers between legitimate parties Alice and Bob. In asymptotic case, we experimentally compare RFI-MDI-QKD protocol with the original MDI-QKD protocol at the transmission distance of 160 km, when the different misalignments of the reference frame are deployed. By considering observables and statistical fluctuations jointly, four-intensity decoy-state RFI-MDI-QKD protocol with biased bases is experimentally achieved at the transmission distance of 100km and 120km. The results show the robustness of our scheme, and the key rate of RFI-MDI-QKD can be improved obviously under a large misalignment of the reference frame.
The reference-frame-independent measurement-device-independent quantum key distribution (RFI-MDI-QKD) protocol is immune to both the slow drift of the reference frame and the potential attacks aimed at the measurement device. However, its reference-frame-independent behavior in terms of performance relies on the assumption that the key-generation basis is well aligned, which may not always be satisfied in practice. In this work, to address this limitation in RFI-MDI-QKD, we propose a fully RFI-MDI-QKD (FRFI-MDI-QKD) protocol by harnessing the quantum discord resource, and prove its security against collective attacks in the asymptotic case. With a 3 × 3 matrix whose singular values are independent of the reference frame, the information obtained by the eavesdropper in FRFI-MDI-QKD is completely irrelevant to the reference frame. Simulation results show that, in the case of a misaligned key-generation basis, FRFI-MDI-QKD can yield more positive keys compared with previous RFI-MDI-QKD; in the case of a well-calibrated key-generation basis, the key rate performance of FRFI-MDI-QKD can be reduced to that of previous RFI-MDI-QKD.
Abstract The robustness of reference-frame-independent measurement-device-independent quantum key distribution (RFI-MDI-QKD) against detection system vulnerabilities and its tolerance to reference frame drifts make it an ideal choice for hybrid channels. However, the impact of atmospheric turbulence on transmittance fluctuations remains a significant challenge for enhancing the performance of RFI-MDI-QKD. In this paper, we apply prefixed-threshold real-time selection and advantage distillation techniques to RFI-MDI-QKD in a hybrid channels scenario. Then, we analytically derive formulas for secret key rate in hybrid channels. Simulation results show that our modified scheme has apparent advances in both maximum tolerant loss and secure key rate compared to the fiber-only channel. Specifically, the result demonstrates that the maximum transmission distance can be improved by 15 km and 28 km when N = 1012 and 1011. Our work not only provides a more robust key distribution protocol but also establishes a solid theoretical foundation for enhancing the performance of RFI-MDI-QKD in hybrid channels.
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.