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Entropy

An Effective Parameter Analysis for Sending-or-Not-Sending Quantum Key Distribution with Untrusted Light Sources

Jiajian Huang, Weigang Li, Yucheng Qiao

Published May 22, 2025• 2 citations
Publisher

Abstract

The twin-field (TF) protocol is a key protocol in quantum key distribution (QKD) that enables remote key distribution, achieving a maximum secure transmission distance of over 500 km. However, the TF protocol still faces several security issues in real-world environments. To address the issue of untrusted sources, one effective solution is to introduce a light-source monitoring module into the system. Analysis shows that a solution based on untagged bits (UBs) can achieve ideal monitoring performance. This solution can capture UB signals to accurately estimate key parameters in the protocol's security analysis, ultimately deriving a tight bound for the secure bit rate. Simulations show that this solution approximates the performance of ideal light sources in the presence of untrusted sources and effectively mitigates the impact of light-source fluctuations. It outperforms other solutions in key performance metrics, such as transmission distance.

DOI
10.3390/e27060547

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The twin-field (TF) protocol is a key protocol in quantum key distribution (QKD) that enables remote key distribution, achieving a maximum secure transmission distance of over 500 km. However, the TF protocol still faces several security issues in real-world environments. To address the issue of untrusted sources, one effective solution is to introduce a light-source monitoring module into the system. Analysis shows that a solution based on untagged bits (UBs) can achieve ideal monitoring performance. This solution can capture UB signals to accurately estimate key parameters in the protocol's security analysis, ultimately deriving a tight bound for the secure bit rate. Simulations show that this solution approximates the performance of ideal light sources in the presence of untrusted sources and effectively mitigates the impact of light-source fluctuations. It outperforms other solutions in key performance metrics, such as transmission distance.
Twin-field quantum key distribution (TF-QKD) is proposed to achieve a remote key distribution with a maximum secure transmission distance up to over 500 km. Although the security of TF-QKD in its detection part is guaranteed, there are some remaining problems in the source part. The sending-or-not-sending (SNS) protocol is proposed to solve the security problem in the phase post-selection process; however, the light source is still assumed to be an ideal coherent state. This assumption is not satisfied in real-life QKD systems, leading to practical secure issues. In this paper, we discuss the condition that the photon number distribution (PND) of the source is unknown for the SNS protocol, demonstrate that the security analysis is still valid under a source with unknown PND, and show that with light source monitoring, the performance of the SNS protocol can remain almost unchanged.
Twin-field (TF) quantum key distribution (QKD) promises high key rates over long distances to beat the rate-distance limit. Here, applying the sending-or-not-sending TF QKD protocol, we experimentally demonstrate a secure key distribution that breaks the absolute key-rate limit of repeaterless QKD over a 509-km-long ultralow loss optical fiber. Two independent lasers are used as sources with remote-frequency-locking technique over the 500-km fiber distance. Practical optical fibers are used as the optical path with appropriate noise filtering; and finite-key effects are considered in the key-rate analysis. The secure key rate obtained at 509 km is more than seven times higher than the relative bound of repeaterless QKD for the same detection loss. The achieved secure key rate is also higher than that of a traditional QKD protocol running with a perfect repeaterless QKD device, even for an infinite number of sent pulses. Our result shows that the protocol and technologies applied in this experiment enable TF QKD to achieve a high secure key rate over a long distribution distance, and is therefore practically useful for field implementation of intercity QKD.
Twin-field (TF) quantum key distribution (QKD) can overcome the fundamental rate-loss bound of repeaterless QKD, enabling secure communication over long distances. However, in practical implementations, its security relies on accurate intensity modulation, which may be compromised by source imperfections and light-injection attacks. In this work, we investigate the security of the NPP TF-QKD protocol in the presence of imperfect intensity modulation, focusing on Trojan-horse attacks and induced photorefractive attacks. By employing the reference technique, we establish a finite-key security proof that explicitly incorporates this source-side information leakage. Numerical simulations show that with realistic transmitter isolation, the NPP TF-QKD protocol can still surpass the rate-loss bound and achieve secret-key rates close to the ideal case. Our results further demonstrate strong robustness against modulation deviations induced by photorefractive effects. These findings confirm the practical security of TF-QKD under realistic source imperfections and provide quantitative guidance for the design of secure quantum communication systems.
The sending-or-not-sending (SNS) protocol is one of the most major variants of the twin-field (TF) quantum key distribution (QKD) protocol and has been realized in a 511-km field fiber, the farthest field experiment to date. In practice, however, all decoy-state methods have unavoidable source errors, and the source errors may be non-random, which compromises the security condition of the existing TF-QKD protocols. In this study, we present a general approach for efficiently calculating the SNS protocol's secure key rate with source errors, by establishing the equivalent protocols through virtual attenuation and the tagged model. This makes the first result for TF QKD in practice where source intensity cannot be controlled exactly. Our method can be combined with the two-way classical communication method such as active odd-parity pairing to further improve the key rate. The numerical results show that if the intensity error is within a few percent, the key rate and secure distance only decrease marginally. The key rate of the recent SNS experiment in the 511-km field fiber is still positive using our method presented here, even if there is a [Formula: see text] intensity fluctuation. This shows that the SNS protocol is robust against source errors.
Abstract Quantum key distribution (QKD) over a point-to-point link enables us to benefit from a genuine quantum effect even with conventional optics tools such as lasers and photon detectors, but its capacity is limited to a linear scaling of the repeaterless bound. Recently, twin-field (TF) QKD was conjectured to beat the limit by using an untrusted central station conducting a single-photon interference detection. So far, the effort to prove the conjecture was confined to the infinite key limit which neglected the time and cost for monitoring an adversary’s act. Here we propose a variant of TF-type QKD protocol equipped with a simple methodology of monitoring to reduce its cost and provide an information-theoretic security proof applicable to finite communication time. We simulate the key rate to show that the protocol beats the linear bound in a reasonable running time of sending 10 12 pulses, which positively solves the conjecture.
Abstract Mode pairing quantum key distribution (MP-QKD) overcomes the repeaterless bound without requiring phase locking and phase tracking. However, MP-QKD still assumes that the light source is trusted, which can present challenges in practical deployments and potentially introduce security vulnerabilities. In this paper, we propose a light source monitoring (LSM) scheme that guarantees the security of MP-QKD with the untrusted light sources. The simulation results demonstrate that, when considering untrusted light sources, the performance of MP-QKD with the LSM scheme remains nearly identical to that of ideal MP-QKD, even in the presence of the source fluctuations. Furthermore, we simplify some of the complex integration calculations involved in simulating the observed quantities of MP-QKD, which reduces the running time of the parameter optimization procedure.