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Optics Express

Reference-frame-independent quantum key distribution with passive decoy states

Yuhang Zhao, Chuan-Hao Shu, ZHANG WEN ZHANG WEN, Jian-Rong Zhu, Chunmei Zhang

Published Feb 4, 2026• 0 citations
Publisher

Abstract

Reference-frame-independent quantum key distribution (RFI-QKD) enables the generation of secure keys when the reference frame suffers from unknown and slow drifting. To combat the potential photon-number-splitting attacks in RFI-QKD, the decoy-state method should be adopted. Generally, the decoy states are prepared by actively modulating different photon numbers of weak coherent pulses, which, however, may leak the side-channel information due to the imperfect modulation. To address this security loophole, we propose to implement the improved RFI-QKD protocol [Opt. Lett.47, 4219 (2022)10.1364/OL.470558], which bounds the eavesdropper's information analytically and is less sensitive to statistical fluctuations, with passive decoy states. By interfering two weak coherent pulses on a beam splitter and then directing one arm of the outputs into the single-photon avalanche detector (SPAD), different photon-number distributions of pulses can be prepared according to the response status of SPAD. To make this scheme more practical, we consider the inevitable afterpulses of the SPADs for both the transmitter and receiver, and construct an afterpulse-compatible analysis model. Simulation results show that our scheme can achieve good performance in practical scenarios.

DOI
10.1364/oe.582664

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Reference-frame-independent quantum key distribution (RFI-QKD) enables the generation of secure keys when the reference frame suffers from unknown and slow drifting. To combat the potential photon-number-splitting attacks in RFI-QKD, the decoy-state method should be adopted. Generally, the decoy states are prepared by actively modulating different photon numbers of weak coherent pulses, which, however, may leak the side-channel information due to the imperfect modulation. To address this security loophole, we propose to implement the improved RFI-QKD protocol [Opt. Lett.47, 4219 (2022)10.1364/OL.470558], which bounds the eavesdropper's information analytically and is less sensitive to statistical fluctuations, with passive decoy states. By interfering two weak coherent pulses on a beam splitter and then directing one arm of the outputs into the single-photon avalanche detector (SPAD), different photon-number distributions of pulses can be prepared according to the response status of SPAD. To make this scheme more practical, we consider the inevitable afterpulses of the SPADs for both the transmitter and receiver, and construct an afterpulse-compatible analysis model. Simulation results show that our scheme can achieve good performance in practical scenarios.
In quantum key distribution (QKD), the users need to share the same reference frame. If their reference frames are inconsistent, the QKD system will not function properly. The most widely used method today is the active real-time calibration of both communication reference frames by using classical communication. In order to get rid of the real-time calibration operation of the reference frames, a QKD protocol independent of reference frame is proposed, called reference-frame-independent QKD (RFI-QKD). The RFI-QKD protocol is immune to the effects of slowly changing reference frame drift, requiring that only one set of bases should be aligned by Alice and Bob, and the remaining two sets of bases can slowly change in the channel. In the real QKD system, a set of basis vectors can always be found to maintain a stable alignment. However, some assumptions are made for the sources in most reported researches, i.e. with a trusted and fixed photon-number distribution (PND), which usually cannot be satisfied in practical implementations. Those unreasonable assumptions will inevitably compromise the security of practical QKD systems. To solve the problem, in this work, we present a passive light source monitoring (PLSM) scheme for RFI-QKD, which is accomplished by a passive monitoring module consisting of a beam splitter and two detectors on the source side. Through the PLSM module, we can have four monitoring events by using two local detectors and then precisely estimate the bounds of source distributions. Specifically, we take the three-intensity decoy-state-based RFI-QKD for example for illustraing the events. Compared with the original RFI-QKD, our PLSM method can passively monitor the PND and has many advantages, with light source fluctuations, finite-size effects and reference frame deflection angles taken into account.
Reference-frame-independent quantum key distribution (RFI-QKD) has been proven to be intrinsically robust against slowly varying reference frames under realistic environment. In this paper, we propose a simplified scheme for the passive decoy-state RFI-QKD considering the afterpulsing effect. We investigated the system performance with the weak coherent source (WCS) and parametric down conversion (PDC) source, respectively. Numerical simulation results show that the simplified scheme can achieve comparable secure key rate with the active decoy-state scheme. Our scheme is advantageous to simplify the system implementation and reduces the time cost. Besides, it is proven that the afterpulsing effect plays dominant role in the system. Our work could provide a useful solution for RFI-QKD in practical situations.
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.
Reference-frame-independent measurement-device-independent quantum key distribution (RFI-MDI-QKD) is proposed to remove all possible detector side channel attacks without the alignment of reference frames. Due to unavoidable multiphoton events in practical sources, the decoy-state method is always adopted in real-life QKD systems. Unlike original MDI-QKD (O-MDI-QKD), the characterization on practical decoy-state RFI-MDI-QKD is still absent to date. In this paper, we investigate the performance of practical decoy-state RFI-MDI-QKD at different misalignments of reference frames with full parameter optimization when considering statistical fluctuations, and provide a clear comparison between decoy-state RFI-MDI-QKD and O-MDI-QKD. Simulation results demonstrate that decoy-state RFI-MDI-QKD can exhibit performance comparable to that of O-MDI-QKD in practical scenarios, which is very robust in QKD systems.
Reference-frame-independent measurement-deviceindependent quantum key distribution (RFI-MDI-QKD) can eschew the alignment of reference frames in practical systems and defeat all potential detector side channel attacks. Here, we propose the decoy-state RFI-MDI-QKD protocol with biased bases. In this protocol, two legitimate parties Alice and Bob prepare signal states in Z, X, and Y bases and decoy states in X and Y bases, which avoids the futility in Z basis for decoy states and simplifies the operation of existing systems. Considering the security against coherent attacks with statistical fluctuations, we investigate the performance of the decoy-state RFI-MDI-QKD protocol with biased bases in the environment of unknown and slowly drifting reference frames and make comparisons with the original decoy-state RFI-MDI-QKD protocol under the same conditions. Simulation results show that the proposed protocol can increase the achievable secret key rate and transmission distance obviously compared with the original protocol, which is very promising in real-life QKD systems.
Reference-frame-independent quantum key distribution (RFI QKD) significantly alleviates alignment requirements for reference frame in practical quantum communication systems. While the original protocol requires Alice to prepare six quantum states in ZZZ, XXX, and YYY bases, its reliance on active modulation introduces inherent side-channel vulnerabilities from device imperfections. We address this security limitation by integrating a fully passive source into the RFI framework. In this paper, we propose a fully passive RFI QKD protocol. Our protocol avoids active modulation entirely, suppressing side-channel risks through passive quantum state generation. Moreover, by making full utilization of the quantum states generated by the fully passive source, we enhance the secure key rate of fully passive protocol. We establish a system model to analyze the performance of the protocol. Through the optimization of post-selection intervals and intensities, we obtain the maximum secure key transmission rate of the protocol. Under ideal circumstances, the secure key transmission rate of our protocol can reach more than 50% of that of the ideal QKD. Under practical conditions, we have considered the finite-length effect. When pulse number generated by the source reaches 101210^{12}1012, the maximum communication distances of the protocol can reach 167 km and 136 km with a reference frame misalignment of $0 $ and $45^{\circ} $ respectively. We believe that our protocol can contribute to the development of practical QKD systems.