Quantum key distribution (QKD) enables the establishment of shared keys between two distant users, Alice and Bob, based on the fundamental principles of quantum mechanics, and it has proven to possess information-theoretic security. In most of QKD systems, Alice and Bob require a shared reference frame, and real-time calibration of the reference frame increases system costs and reduces its performance. Fortunately, the reference-frame-independent QKD protocol has been proposed, overcoming reference-frame drift issues and receiving widespread attention. However, in practical QKD systems, the non-ideal characteristics of realistic devices introduce certain inconsistency between the theory and the practice. In real-world quantum key distribution systems, device imperfections can lead to security vulnerabilities, thereby reducing system security. For example, imperfections in the encoding apparatus at the source end may result in errors in the quantum states. The inherent defects in the detection part may cause after-pulse effects and dead-time effects, thus reducing the key rate. Therefore, in this work, we propose a practical state-preparation error tolerant reference-frame-independent quantum key distribution protocol by taking imperfections in both the source and the detectors into account. Moreover, a three-intensity decoy-state scheme for modeling analysis and numerical simulations is employed. In this protocol, we reduce the influence of state-preparation errors on the key rate by utilizing virtual state methods to precisely estimate the phase-error rate. Furthermore, by characterizing the effects of after-pulses and dead-time on the key rate, our protocol exhibits higher robustness and can effectively address issues related to detector imperfections. This approach can also be extended to other quantum key distribution protocols with higher security levels, such as measurement-device-independent quantum key distribution protocol and twin-field quantum key distribution, further mitigating the influence of device imperfections on practical implementation of QKD system. Therefore, our present work provide important reference value for putting the quantum key distributions into practical application.
Quantum key distribution (QKD) enables the establishment of shared keys between two distant users, Alice and Bob, based on the fundamental principles of quantum mechanics, and it has proven to possess information-theoretic security. In most of QKD systems, Alice and Bob require a shared reference frame, and real-time calibration of the reference frame increases system costs and reduces its performance. Fortunately, the reference-frame-independent QKD protocol has been proposed, overcoming reference-frame drift issues and receiving widespread attention. However, in practical QKD systems, the non-ideal characteristics of realistic devices introduce certain inconsistency between the theory and the practice. In real-world quantum key distribution systems, device imperfections can lead to security vulnerabilities, thereby reducing system security. For example, imperfections in the encoding apparatus at the source end may result in errors in the quantum states. The inherent defects in the detection part may cause after-pulse effects and dead-time effects, thus reducing the key rate. Therefore, in this work, we propose a practical state-preparation error tolerant reference-frame-independent quantum key distribution protocol by taking imperfections in both the source and the detectors into account. Moreover, a three-intensity decoy-state scheme for modeling analysis and numerical simulations is employed. In this protocol, we reduce the influence of state-preparation errors on the key rate by utilizing virtual state methods to precisely estimate the phase-error rate. Furthermore, by characterizing the effects of after-pulses and dead-time on the key rate, our protocol exhibits higher robustness and can effectively address issues related to detector imperfections. This approach can also be extended to other quantum key distribution protocols with higher security levels, such as measurement-device-independent quantum key distribution protocol and twin-field quantum key distribution, further mitigating the influence of device imperfections on practical implementation of QKD system. Therefore, our present work provide important reference value for putting the quantum key distributions into practical application.
The quantum digital signature (QDS) has attracted much attention as it ensures the nonrepudiation, unforgeability, and transferability of signature messages based on information-theoretic security. Amiri et al. ( Phys. Rev. A 93 032325 ) proposed the first practical QDS protocol based on orthogonal coding, which has realized information-theoretic security and become the mainstream paradigm in QDS research. The procedure of QDS involves two essential stages, the one is the distribution stage, in which Alice-Bob and Alice-Charlie individually utilize the three-intensity decoy-state quantum key distribution protocol but without error correction or privacy amplification, namely, key-generation protocol, to generate correlated bit strings, the other is the messaging stage, in which Alice transmits signature messages to the two recipients. However, previous theoretical and experimental studies both overlooked the modulation errors that may be introduced in the state preparation process due to the imperfections in modulator devices. Under the traditional framework of GLLP analysis method, these errors will significantly reduce the actual signature rates. Therefore, we propose a state-preparation-error tolerant QDS and use parameter analysis to characterize the state preparation error to make the simulation analysis more realistic. In addition, we analyze the signature rates of the present scheme by using the three-intensity decoy-state method. Compared with previous QDS protocols, our protocol almost shows no performance degradation under practical state preparation errors and exhibits a maximum transmission distance around 180 km. Furthermore, state preparation errors do not have a significant influence on the bit error rate induced by normal communication between the legitimate users or the one produced by an eavesdropper. These results prove that the method proposed in this paper has excellent robustness against state preparation errors and it can achieve much higher signature rates and signature distances than other standard methods. Besides, signature rates are basically unchanged under different total pulse numbers, which shows that our protocol also has good robustness against the finite-size effect. Additionally, in the key generation process, our method is only required to prepare three quantum states, which will reduce the difficulty of experiment realizations. Furthermore, the proposed method can also be combined with the measurement-device-independent QDS protocol and the twin-field QDS protocol to further increase the security level of QDS protocol. Therefore, our work will provide an important reference value for realizing the practical application of QDS in the future.
In practical quantum key distribution systems, there inevitably exist errors in the quantum state preparation process due to imperfections in realistic equipment and devices. Those errors would lead to some security loopholes in the quantum key distribution systems. According to the work of Tamaki et al. ( Phys. Rev. A 90 052314 ), here in this work we propose a state preparation error tolerant quantum key distribution protocol through using heralded single-photon sources. In this protocol, we characterize the size of the error in the preparation state of Alice and bring it into the security analysis, thereby avoiding possible security loopholes and improving the security of the system. Moreover, we take the three-intensity decoy-state method for example to introduce the method of constructing the model and estimating the parameters, and carry out corresponding numerical simulations. We make a comparison between the loss tolerant protocol with weak coherent source (WCS) and our present protocol using heralded single-photon source (HSPS). Simulation results show that under the same state preparation error, the key generation rate of the protocol based on WCS is higher than that of protocol based on HSPS at short transmission distances (e.g. less than 150 km). The main reason is that the detection efficiency of the local detector used in the latter scheme is low. However, in the case of long transmission distances (e.g. greater than 200 km), the key generation rate of scheme with WCS drops deeply, while the decline of the key generation rate of the present scheme is much flatter. As a result, the former can no longer generate keys after 211 km, while the latter can transmit a maximum distance of 228 km. Moreover, we also make a comparison between the present scheme and the GLLP protocol with HSPS. The simulation results show that the GLLP protocol with HSPS is very sensitive to the state preparation error and its key generation rate will rapidly decrease with the increase of the state preparation error. On the contrary, our present protocol shows almost no performance degradation under practical state preparation errors. It thus verify the robustness against the state preparation errors of our present work. In addition, in principle, the method can also be combined with the measurement-device-independent quantum key distribution protocol and the twin-field quantum key distribution protocol to further increase the secure communication transmission distance that the present system can reach. Therefore, this work may provide an important reference value for the practical application of long-distance quantum secure communication in the near future.
Multipartite quantum key distribution (QKD) is a promising area of quantum networks that provides unconditional secret keys among multiple parties, enabling only legitimate users to decrypt the encrypted message. However, security proofs of existing multipartite QKD typically assume perfect state preparation devices of legitimate users and neglect the relative rotation of reference frames. These presumptions are, nevertheless, very difficult to meet in practice, and thus the security of current multipartite QKD implementations is not guaranteed. By combining the idea of a loss tolerant technique, introduced by Tamaki et al. (K. Tamaki et al., Phys. Rev. A, 90, 052314, 2014), and the concept of a reference frame-independent protocol, we propose a three-party QKD protocol that considers state preparation flaws and the slow drift of reference frames. Through a numerical simulation, the influence of misaliged reference frames on the protocol’s stability was examined by drifting reference frames through angles β=π/5, β=π/6 and β=π/7. In addition, the performance of the proposed protocol was examined for the encoding flaws set at δ=0.35, δ=0.20, and δ=0.10. The results show that the protocol is robust against state preparation flaws, and is insignificantly impacted by misalignment of the reference frames because the achieved transmission distances and secret key rates are comparable to the perfect scenarios. This work dramatically contributes toward the realization of practical and secure multipartite QKD. The proposed protocol has direct applications in quantum communication network environments that involve unknown and slowly varying reference frames, web conferences, and online communications.
Abstract The trade-off between distance and secret key generation rate remains one of the major challenges in the practical implementation of quantum key distribution (QKD). As a solution, a twin field QKD protocol was proposed by Lucamarini et al (2018) to address this challenge. In this protocol, the achievable secret key rate scales with the square root of channel transmittance and can surpass the secret key capacity for repeaterless QKD. However, the protocol exploits phase to encode information which presents the problem of active stabilization of interferometers. We propose a reference frame independent twin field quantum key distribution (RFITF QKD), which does not require the reference frames’ alignment. Thus, this reduces the complexity of practical QKD systems in achieving active stabilization of phase. Moreover, we employ the loss-tolerant method proposed by Tamaki et al (2014) which allows us to prove the security of the protocol by considering imperfections in the state preparation. Our simulation results show that our proposed protocol can extract a secure key over a transmission distance of l = 505 km, l = 516 km and l = 530 km for deviation of 8.42°, 7.28° and 5.15°, respectively from the desired phase encoding angle. These results demonstrate that despite the state preparation flaws, the key rates achieved are still comparable to the perfect encoding scenario. When our proposed protocol is implemented with an imperfect source, it achieves a transmission distance beyond the secret key capacity bound for repeaterless QKD.
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.
Quantum Key Distribution (QKD) offers information-theoretic security grounded in the laws of quantum mechanics rather than computational assumptions. While its theoretical foundations are robust, practical implementations necessarily deviate from the idealized models assumed in security analyses, opening the door to side-channel attacks and implementation loopholes. In particular, most research to date has focused on mitigating vulnerabilities in the measurement devices, leading to the development of Measurement-Device-Independent QKD (MDI-QKD) and Twin-Field QKD (TF-QKD), which effectively close all receiver-side loopholes. By contrast, the security of the source has remained less explored, despite being critical for the overall integrity of QKD systems. The goal of this thesis is to develop security proofs that explicitly account for realistic imperfections in QKD sources. Special emphasis is placed on three main aspects: correlations between emitted pulses that violate independence assumptions, imperfect phase randomization arising from practical modulation schemes, and leakage of internal settings through passive or active side channels. By formulating rigorous methods to analyze these imperfections, the work aims to provide a framework that enables practitioners to quantify and mitigate implementation risks systematically. Additionally, this thesis seeks to clarify under which conditions the commonly used decoy-state method remains secure, and to what extent source assumptions can be relaxed without compromising performance. This thesis aims to advance the understanding of how real-world deviations impact QKD security and to contribute to the development of protocols and devices. Ultimately, this work is motivated by the ambition to help bring QKD from a theoretically promising idea to a mature technology deployable with confidence in practical scenarios.