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Acta Physica Sinica

Reference-frame-independent quantum key distribution based on passive light source monitoring

Jiayi Zhang, Hua-Xing Chen, Huan-Yu Zhang, Xue-Rui Qian, Chunhui Zhang, Qin Wang

Published Jan 1, 2023• 1 citation

Abstract

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.

DOI: 10.7498/aps.72.20230609

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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) 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.

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

Z

,

X

, and

Y

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

10^{12}

, 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.

Reference frame independent quantum key distribution (RFI-QKD) allows two legitimate parties to share the common secret keys with the drift of reference frames. In order to reduce the actual requirements of RFI-QKD protocol on light source and make it more suitable for practical applications, this paper gives a specific description of RFI-QKD protocol with an untrusted source and analyzes the practical security of this protocol based on the two-way “plug and play” structure commonly used in practical systems. In addition, we also investigate the performance of RFI-QKD with an untrusted source considering statistical fluctuations based on Chernoff bound. Using simulations, we compare the secret key rate of RFI-QKD with an untrusted source to RFI-QKD with trusted source. The results show that the performance of RFI-QKD with an untrusted source is similar to that of RFI-QKD with trusted source, and the finite data size clearly effects the performance of our protocol.

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.

Twin-field quantum key distribution (TF-QKD) can break the repeaterless linear bound and possess the measurement-device-independent security, and thus seems very promising in practical applications of quantum secure communication. In most reported TF-QKD protocols, light sources are assumed to possess trusted and fixed photon number distributions (PND), which are unrealistic assumptions in practical applications. Fortunately, the light source monitoring (LSM) method is proposed to circumvent this problem by actively adjusting the attenuation coefficient and monitoring the photon number distribution of light sources. However, the active light source monitoring (ALSM) method may induce additional modulation errors due to imperfect attenuation devices, deteriorating practical performances of TF-QKD systems. In this manuscript, we propose a passive light source monitoring (PLSM) scheme for TF-QKD, and employ the sending-or-not-sending (SNS) TF-QKD as an example for illustration. Simulation results show that our present work can greatly exceed both the original SNS protocol and the ALSM scheme when light source fluctuations and modulation errors are taken into account.

Reference-frame-independent quantum key distribution (RFI-QKD) has gained widespread attention due to its unique advantage for practical application, as it circumvents the need for active reference-frame alignment within the system. However, in comparison to the standard BB84 protocol, the original six-state RFI protocol requires a greater number of quantum states to be operated by Alice and Bob, which is an aspect that merits optimization. In this work, we propose a four-state RFI protocol and illustrate that Alice and Bob each require only four quantum states to perform channel estimation that remains independent of reference-frame deviation, which can proficiently reduce the system complexity. Furthermore, through numerical simulations taking the finite-key-size effect into consideration, we show that the four-state RFI protocol can achieve a secure key rate and transmission distance on par with those of the original six-state RFI protocol. Finally, an experiment over 200 km is conducted to evaluate the feasibility of our scheme. We believe that our protocol can streamline the implementation of RFI-QKD and thereby contribute to the practical advancement of RFI-QKD.