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Acta Physica Sinica

Influence of source intensity errors in unidimensional Gaussian modulation continuous-variable quantum key distribution

Pu Perry Wang, Zengliang BAI, Chang Li-Wei

Published Jan 1, 2025• 2 citations
Publisher

Abstract

Unidimensional Gaussian modulation continuous-variable quantum key distribution (UD CV-QKD) uses only one modulator to encode information. The UD CV-QKD has the advantages of low implementation cost and low random number consumption, making it attractive for the construction of future miniaturized and low-cost large-scale quantum communication networks. However, in the actual application of the protocol, the intensity fluctuation of the source pulsed light, device defects, and external environmental interference maybe lead to the generation of source intensity errors, thereby affecting the realistic security and performance of the protocol. To solve these problems, the security and performance of UD CV-QKD are studied in depth under source intensity errors in this work. The mechanism of source intensity errors influencing the protocol parameter estimation process is analyzed. To make it possible that the protocol can operate stably under various realistic conditions and ensure communication security, three practical assumptions about the sender’s abilities are made in this work, and corresponding data optimization processing schemes for these assumptions are proposed to reduce the negative influence of source intensity errors. Additionally, both source errors and finite-size effect are comprehensively considered to ensure the realistic security of the system. The simulation results indicate that the source intensity errors cannot be neglected and the maximum transmission distance of the system will be reduced by approximately 20 km for significant intensity fluctuations. Therefore, in the practical implementation of the protocol, the influence of source intensity errors must be fully considered, and the corresponding countermeasures should be taken to reduce or even eliminate these errors. This study provides theoretical guidance for securely implementing the UD CV-QKD in real-world environments.

DOI
10.7498/aps.74.20250025

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Unidimensional Gaussian modulation continuous-variable quantum key distribution (UD CV-QKD) uses only one modulator to encode information. The UD CV-QKD has the advantages of low implementation cost and low random number consumption, making it attractive for the construction of future miniaturized and low-cost large-scale quantum communication networks. However, in the actual application of the protocol, the intensity fluctuation of the source pulsed light, device defects, and external environmental interference maybe lead to the generation of source intensity errors, thereby affecting the realistic security and performance of the protocol. To solve these problems, the security and performance of UD CV-QKD are studied in depth under source intensity errors in this work. The mechanism of source intensity errors influencing the protocol parameter estimation process is analyzed. To make it possible that the protocol can operate stably under various realistic conditions and ensure communication security, three practical assumptions about the sender’s abilities are made in this work, and corresponding data optimization processing schemes for these assumptions are proposed to reduce the negative influence of source intensity errors. Additionally, both source errors and finite-size effect are comprehensively considered to ensure the realistic security of the system. The simulation results indicate that the source intensity errors cannot be neglected and the maximum transmission distance of the system will be reduced by approximately 20 km for significant intensity fluctuations. Therefore, in the practical implementation of the protocol, the influence of source intensity errors must be fully considered, and the corresponding countermeasures should be taken to reduce or even eliminate these errors. This study provides theoretical guidance for securely implementing the UD CV-QKD in real-world environments.
To address the demand for low-cost deployment in quantum key distribution (QKD) networks, this study explores the implementation of unidimensional (UD) modulation continuous-variable quantum key distribution (CV-QKD) protocols within downstream access networks. The UD CV-QKD protocol employs a single modulator for information encoding, offering benefits such as reduced implementation cost and lower random number consumption, which collectively decrease the overall setup expense of QKD systems. Through systematic performance analysis, it is demonstrated that the proposed UD modulation downstream access network scheme exhibits strong scalability and practical applicability. When supporting 32 users, the system maintains secure communication over transmission distances of up to 50 km. As the number of users increases to 64, performance declines slightly; however, the system still achieves a 35 km transmission distance, which remains suitable for many metropolitan access applications. Even in high-density access scenarios involving 128 users, the system sustains a positive key rate within a transmission range of 20 km. Furthermore, this study evaluates the protocol’s practical security under source intensity errors and finite-size effects. These results provide meaningful guidance for deploying low-cost, high-security quantum communication access networks and contribute to advancing QKD technologies toward scalable, real-world implementations.
Continuous-variable quantum key distribution (CV-QKD), which uses quadratures of the electromagnetic field, enables practical quantum communication using standard telecommunication technologies. Unidimensional CV-QKD (UD-CVQKD) simplifies the implementation by restricting modulation to a single quadrature. In this work, we experimentally demonstrate a free-space Gaussian-modulated UD-CVQKD system operating under a high detector electronic-noise regime (1.4 shot-noise units). The system employs polarized coherent states with signal and local oscillator co-propagating in the same spatial mode in orthogonal polarizations, ensuring stable interference. System security is analyzed under both untrusted (UTD) and trusted (TD) detector noise models. While no positive secret key rate is obtained under the UTD model, the TD model enables secure key generation over a finite range of modulation variances, highlighting the critical role of detector trust in high-noise conditions. A maximum secret key rate of 270 kbps is achieved at an optimal modulation variance of 11.57. Furthermore, secure operation requires high-transmittance (low-loss) channels under such noise conditions. This study demonstrates the practical feasibility of free-space UD-CVQKD in realistic high electronic-noise detection constraints and highlights detector electronic noise as a key limiting factor in practical systems.
Continuous-variable measurement-device-independent quantum key distribution (CV-MDI-QKD) is immune to all detector side channel attacks, however its security requires trusted sources. We investigate the effects of source intensity errors, the most crucial source error, on the security of CV-MDI-QKD protocol with Gaussian-modulated coherent states. We establish a general source intensity errors model and derive the secret key rate based on different assumptions on the abilities of legal parties Alice and Bob. To avoid the adverse effects of the sources' intensity errors on CV-MDI-QKD, we present different data-processing schemes. We also assess the security of the protocol against collective Gaussian attacks in the finite-size scenario with composable security. Taking source intensity errors into consideration, we achieve improved security compared to previous demonstrations. Our results will provide a useful reference for practical implementations of CV-MDI-QKD.
Continuous-variable measurement-device-independent quantum key distribution (CV-MDI QKD) can fundamentally defend all attacks on the measurement devices. Consequently, higher requirements are put forward for the source of a CV-MDI QKD system. However, the imperfections of the actual source brings practical security risks to the CV-MDI QKD system. Therefore, the characteristics of the realistic source must be controlled in real time to guarantee the practical security of the CV-MDI QKD system. Here we propose a countermeasure for negative impact introduced by the actual source in the CV-MDI QKD system based on the one-time-calibration method, not only eliminating the loophole induced from the relative intensity noise (RIN), which is part of the source noise, but also modeling the source noise thus improves the performance. In particular, three cases in terms of whether the preparation noise of the practical sources are defined or not, where only one of the users or both of the two users operate monitoring on their respective source outputs, are investigated. The simulation results show that the estimated secret key rate without our proposed scheme is about 10.7 times higher than the realistic rate at 18 km transmission distance when the variance of RIN is only 0.4. What is worse, the difference becomes greater and greater with the increase of the variance of RIN. Thus, our proposed scheme makes sense in further completing the practical security of the CV-MDI QKD system. In other words, our work enables the CV-MDI QKD system not only to resist all attacks against detectors, but also to close the vulnerability caused by the actual source, thus making the scheme closer to practical security.
Unidimensional-modulation continuous-variable quantum key distribution has received considerable attention due to its simplified transmitter architecture, reduced random-number consumption, and low deployment cost. However, its security against source-side light-injection attacks remains unexplored. In this paper, the effects of such attacks on unidimensional-modulation continuous-variable quantum key distribution systems are systematically investigated. A theoretical model of quantum-state preparation at the transmitter under light-injection attacks is established, parameter estimation bias formulas are derived, the resulting degradation in the secret key rate is quantified, and the theoretical results are validated through numerical simulations. In addition, the security implications of light-injection attacks in the finite-size regime are examined. The results demonstrate that light-injection attacks cause overestimation of the channel transmittance and underestimation of excess noise. Under finite-size conditions, these attacks reduce the minimum data-block length required to achieve a positive secret key rate, thereby creating a false indication of security even when no secure key can actually be generated. These findings demonstrate that light-injection attacks constitute a serious threat to unidimensional-modulation continuous-variable quantum key distribution systems and provide an important theoretical foundation for future secure practical deployment.
Continuous-variable quantum key distribution (CV–QKD) is a system that provides secret keys for symmetric key systems. In the application of CV–QKD, the practical security of the system is crucial. In this article, we investigate the practical security issues caused by non–ideal Gaussian modulation, which is caused by fitting defects of the amplitude modulator’s (AM) modulation curve. We provide the effect of fitting error on parameter estimation. We also give the relationship between the fitting order and the secret key rate. The simulation results indicate that the system is completely unable to communicate during first–order fitting. During second–order fitting, the system’s performance decreases by more than half. During third–order fitting, the system’s performance will be consistent with the ideal. Therefore, to ensure the performance of the CV–QKD system, the fitting order must be at least three or higher.