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New Journal of Physics

Phase-Matching Quantum Key Distribution with Heralded Single-Photon Sources and Local Detection

Shiya Zeng, Ruobin Zhao, Junyan Luo, Zhiwei Sun, Tingting Song

Published Oct 23, 2026• 0 citations
Publisher

Abstract

Abstract Channel loss in long-distance phase-matching quantum key distribution (PM-QKD) amplifies vacuum emissions and dark counts, impairing parameter estimation and limiting secure transmission distance. In this paper, we propose a PM-QKD protocol based on heralded single-photon sources (HSPSs) with local detection. In the key sifting stage, local heralding outcomes are filtered to suppress vacuum-dominated noise and enhance the single-photon fraction of the retained ensemble. A three-intensity decoy-state method is used to estimate the single-photon contribution and bound the phase-error rate. An asymptotic security analysis is provided. Simulation results show that the proposed protocol surpasses the PLOB bound at $316\,\mathrm{km}$ and achieves a practical key rate of $10^{-8}$ at $496\,\mathrm{km}$, while the conventional PM-QKD protocol based on weak coherent sources reaches the same key rate only at $439\,\mathrm{km}$. These gains are mainly attributed to the vacuum-event filtering strategy, which effectively improves both key-rate performance and transmission distance. Furthermore, our evaluation of a practical threshold detector implementation demonstrates that photon-number-resolving (PNR) detectors are not mandatory to achieve this advantage.

DOI
10.1088/1367-2630/aeb8b4

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Abstract Channel loss in long-distance phase-matching quantum key distribution (PM-QKD) amplifies vacuum emissions and dark counts, impairing parameter estimation and limiting secure transmission distance. In this paper, we propose a PM-QKD protocol based on heralded single-photon sources (HSPSs) with local detection. In the key sifting stage, local heralding outcomes are filtered to suppress vacuum-dominated noise and enhance the single-photon fraction of the retained ensemble. A three-intensity decoy-state method is used to estimate the single-photon contribution and bound the phase-error rate. An asymptotic security analysis is provided. Simulation results show that the proposed protocol surpasses the PLOB bound at 316 km316\,\mathrm{km}316km and achieves a practical key rate of 10−810^{-8}10−8 at 496 km496\,\mathrm{km}496km, while the conventional PM-QKD protocol based on weak coherent sources reaches the same key rate only at 439 km439\,\mathrm{km}439km. These gains are mainly attributed to the vacuum-event filtering strategy, which effectively improves both key-rate performance and transmission distance. Furthermore, our evaluation of a practical threshold detector implementation demonstrates that photon-number-resolving (PNR) detectors are not mandatory to achieve this advantage.
Mode-pairing quantum key distribution (MP-QKD) is a promising protocol immune to detector side-channel attacks and capable of breaking the repeaterless PLOB bound without global phase locking. Existing MP-QKD protocols employ weak coherent sources (WCSs) with a low probability of single-photon emission, hindering MP-QKD's performance improvement. We propose a new, to the best of our knowledge, MP-QKD protocol using the heralded single-photon source (HSPS) to significantly reduce the vacuum emission probability and increase the single-photon emission rate. Compared with the original WCS-MP-QKD protocol, this protocol has three advantages. First, its maximum transmission distance is extended from 488 km to 560 km. Second, the key rates at 100, 200, 300, and 400 km are 4.4 to 7.4 times those of the original protocol. Third, it does not change the original architecture of MP-QKD and is easy to implement experimentally. This HSPS-MP-QKD protocol has application potential in future metropolitan area QKD networks.
For the Bennett-Brassard 1984 (BB84) quantum key distribution, longer distance and higher key generation rate is shown with a heralded single photon source (HSPS). In this paper, the nonorthogonal encoding protocol SARG04 based on one vacuum and two weak decoy states with HSPS is presented. According to the public announcement of Alice's detection events, the overall gain of Bob's detector and quantum bit error rate (QBER) can be divided into two groups, triggered components and nontriggered components. We present a new protocol that use both triggered and nontriggered components to estimate the fraction and QBER of single-photon and two-photon pulses, and then deduce the final secure key generation rate. The final key generation rate over transmission distance is simulated, which shows that we can obtain a higher key rate than that of the existing methods.
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.
Increasing the bit rate and transmission distance of quantum key distribution (QKD) without quantum repeaters is a formidable challenge, which is limited by the secret-key capacity (SKC). Fortunately, phase-matching QKD (PM-QKD) can overcome this limitation by matching the phase of two coherent states and encoding the key information into the common phase. But the probability of the weak coherent source (WCS) sending a single photon is small, so studying the QKD of different signal sources is one of the effective ways to improve the performance of the QKD protocol. The single-photon-added coherent state (SPACS) has a high probability of sending single photons and is closer to an ideal single-photon source than WCS. We have done simulations combining the advantages of the source with the advantages of PM-QKD. Numerical simulations show that the SPACS-PM-QKD protocol also has the ability to break the SKC, and using the SPACS is better in terms of communication distance and key rate compared to WCS.
Twin-field quantum key distribution (TF-QKD) can overcome the fundamental rate-loss limit in the point-to-point QKD without a quantum repeater and achieve high key rates over long distances. However, TF-QKD protocol and its variants commonly use weak coherent pulses (WCPs) as light sources. The vacuum part of WCP accounts for a large proportion, resulting in the lower photon detection rate of the communication receiver, which leads to a shorter transmission distance of the secret key. In this paper, we propose an active-decoy TF-QKD protocol with heralded single-photon source (HSPS), which can achieve higher key rate and longer transmission distance than the active-decoy TF-QKD protocol with WCPs. Also, in order to resist the side channel attacks caused by actively modulating intensity of the pulses, we propose a passive-decoy TF-QKD protocol with HSPS to enhance the security, which can perform almost as good as the active-decoy TF-QKD protocol with WCPs.
The phase-matching quantum key distribution (PM-QKD), one of the variants of Twin-Field (TF) QKD protocol, was recently proposed to overcome the rate-distance limits of point to point protocol without quantum repeaters. In this paper, we propose a more practical PM-QKD protocol version with four-intensity decoy states and source errors, since neither the infinite decoy states nor the precise control of the light source is available in practice. We present the formulation of the secure key rate of the proposed protocol and analyze the performances of the protocol with and without source errors by numerical simulations.