Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

IEEE photonics journal

Practical Measurement Angular Errors Analysis for Thermal-State Continuous-Variable Quantum Key Distribution

Yue Ren, Peiyu Xu, Yundi Huang, Xiangyu Wang, Song Yu

Published Aug 1, 2022• 0 citations
Publisher

Abstract

Thermal-state continuous-variable quantum key distribution (CV-QKD) of direct reconciliation with heterodyne detection can improve the robustness of the protocols. However, CV-QKD protocols require outlier detection, optical phase shifters are used to achieve orthogonal differentiation of the modes, but the actual optical phase shifters suffer from measurement angular errors, resulting in the imperfect phase. This kind of error degrades the security of the system. In this paper, we analyze the causes of measurement angular error and its impact on the secret key rate of the thermal-state CV-QKD protocols. We propose a compensation method to compensate for the effects of the measurement angular error and give a more complete secure analysis method under collective attack. The results obtained in this paper further improve the secure analysis under the thermal-state protocol and further enhance the performance of the system using the compensation method.

DOI
10.1109/jphot.2022.3196010

Related papers

Strengthening practical continuous-variable quantum key distribution against measurement angular error

Tao Shen, Yundi Huang, Xiangyu Wang +3 more

The optical phase shifter that constantly rotates the local oscillator phase is a necessity in continuous-variable quantum key distribution systems with heterodyne detection. In previous experimental implementations, the optical phase shifter is generally regarded as an ideal passive optical device that perfectly rotates the phase of the electromagnetic wave of 90 ∘ . However, the optical phase shifter in practice introduces imperfections, mainly the measurement angular error, which inevitably deteriorates the security of the practical systems. Here, we will give a concrete interpretation of measurement angular error in practical systems and the corresponding entanglement-based description. Subsequently, from the parameter estimation, we deduce the overestimated excess noise and the underestimated transmittance, which lead to a reduction in the final secret key rate. Simultaneously, we propose an estimation method of the measurement angular error. Next, the practical security analysis is provided in detail, and the effect of the measurement angular error and its corresponding compensation scheme are demonstrated. We conclude that measurement angular error severely degrades the security, but the proposed calibration and compensation method can significantly help improve the performance of the practical CV-QKD systems.

arXiv:2107.01798•Optics Express•Sep 3, 2021•8 citations

Practical Imperfections Affecting the Performance of CV-QKD Based on Coherent Detection

Nuno A. Silva, Daniel Pereira, Nelson Jesus Muga +1 more

Continuous variable-quantum key distribution (CV-QKD) based on coherent detection has potential to be a cost-effective solution to deploy secure keys over optical networks. This is due to its compatibility with mature optical communication technologies, such as homodyne and heterodyne detection schemes. Nevertheless, realistic implementations of CV-QKD systems suffer from imperfections in the practical devices used to generate and detect the coherent states. Those imperfections deteriorate the performance of the CV-QKD system and can be exploited by an eavesdropper to steal key information without being detected. In this work, we discuss the impact of practical device imperfections on the excess noise of the CV-QKD and on the achievable transmission distance. We also analyze the impact of detection imperfections on the measurement of the shot noise, and its impact on CV-QKD system security.

International Conference on Transparent Optical Networks•Jul 1, 2020•8 citations

Finite-size security of continuous-variable quantum key distribution with imperfect heterodyne measurement

Adnan A. E. Hajomer, Akash nag Oruganti, Ivan D. Derkach +3 more

Continuous-variable quantum key distribution (CV-QKD) using coherent states and heterodyne detection enables secure quantum communication based on technology that has large similarities to coherent optical telecommunication. Yet, practical implementations of coherent receivers used in both technologies encounter device imperfections, which for CV-QKD are often not addressed in security proofs. Here, we present a theoretical framework that rigorously accounts for imperfect heterodyne measurements arising from phase and amplitude imbalances in the coherent (heterodyne) receiver. Focusing on collective attacks, we establish a finite-size security proof that reveals how measurement imperfections limit the distance over which a positive key rate is achievable. To mitigate these effects, we propose a local transformation during classical post-processing. We validate our approach experimentally on a CV-QKD system with an imperfect coherent receiver, underscoring its potential for scalable, cost-effective CV-QKD with photonic integrated receivers in which phase and amplitude imbalances naturally appear through manufacturing tolerances.

arXiv:2501.10278•Photonics Research•Sep 23, 2025•1 citation

Continuous-variable measurement-device-independent quantum key distribution using modulated squeezed states and optical amplifiers

Pu Wang, Xuyang Wang, Yongmin Li

The measurement-device-independent quantum key distribution (MDI-QKD) protocol is immune to imperfect measurement devices. However, its practicality and performance when implemented in continuous-variable (CV) mode are still not satisfactory. We propose a CV-MDI-QKD protocol based on modulated squeezed states, and analyze its security against two-mode Gaussian attack. The results show that the protocol can achieve a higher secret key rate and transmission distance than previous coherent-state and squeezed-state protocols. A method to compensate the imperfection of a practical homodyne detector using phase-sensitive optical amplifiers is also presented. By setting an appropriate optical amplification gain, realistic detectors with ordinary quantum efficiency can be employed. In addition, we discuss the impact of finite-size effects on the secret key rate of the protocol. The methods presented may aid in the practical application of the CV-MDI-QKD protocol.

Physical Review A•Apr 3, 2019•35 citations

Continuous-mode analysis for practical continuous-variable quantum key distribution

Yanhao Sun, Jiayu Ma, Xiangyu Wang +3 more

Continuous-variable quantum key distribution (CV-QKD) enables two remote parties to establish information-theoretically secure keys and offers high practical feasibility due to its compatibility with mature coherent optical communication technologies. However, as CV-QKD systems progress toward digital implementations, device nonidealities drive the optical field from a single-mode to a continuous-mode region, thereby underscoring the mismatch between theoretical models and practical systems. Here, we introduce temporal modes to construct an entanglement-based scheme that more accurately captures device nonidealities and develop a corresponding secret key rate calculation method applicable to continuous-mode scenarios. We demonstrate that optimizing the pulse-shaping format can significantly improve performance under detector-bandwidth-limited conditions. Experimental results also confirm that the proposed model effectively describes the impact of sampling-time deviations. We further analyze a linear weighted-reconstruction digital signal processing method,which improves the secret key rate by approximately 50% in a 30-km fiber experiment without requiring additional hardware, demonstrating a substantial performance enhancement at metropolitan distances. The proposed theoretical framework accommodates a broader range of experimental conditions and can guide the optimization of digital CV-QKD systems.

quant-pharXiv:2512.15301•Dec 18, 2025•0 citations

Security bound of continuous-variable measurement-device-independent quantum key distribution with imperfect phase reference calibration

Hongxin Ma, Peng Huang, Tao Wang +4 more

Phase reference calibration is a necessary procedure in practical continuous-variable measurement-device-independent quantum key distribution (CV-MDI-QKD) for the need of Bell-state measurement. However, the phase reference calibration may become imperfect in practical applications. We explored the practical security of CV-MDI-QKD with imperfect phase reference calibration under realistic conditions of lossy and noisy quantum channels. Specifically, a comprehensive framework is developed to model and characterize the imperfection of the practical phase reference calibration operation, which is mainly caused by the nonsynchronization of two remote lasers in senders. Security analysis shows that the imperfect phase reference calibration has significant side effects on the performance and security of the CV-MDI-QKD protocol. A tight security bound to thermal excess noise introduced by imperfect phase reference calibration is derived for reverse reconciliation against one-mode collective Gaussian attack in the asymptotic limit, and the upper threshold of this imperfection tolerated by the system is obtained. This security analysis framework can eliminate the security hazards caused by imperfect phase reference calibration without changing the existing CV-MDI-QKD system structure. In addition, this work will improve the practical security framework of CV-MDI-QKD protocol and provide theoretic instruction for the experimental implementation of CV-MDI-QKD protocol.

arXiv:1904.09786•Physical Review A•Nov 25, 2019•8 citations
Thermal-state continuous-variable quantum key distribution (CV-QKD) of direct reconciliation with heterodyne detection can improve the robustness of the protocols. However, CV-QKD protocols require outlier detection, optical phase shifters are used to achieve orthogonal differentiation of the modes, but the actual optical phase shifters suffer from measurement angular errors, resulting in the imperfect phase. This kind of error degrades the security of the system. In this paper, we analyze the causes of measurement angular error and its impact on the secret key rate of the thermal-state CV-QKD protocols. We propose a compensation method to compensate for the effects of the measurement angular error and give a more complete secure analysis method under collective attack. The results obtained in this paper further improve the secure analysis under the thermal-state protocol and further enhance the performance of the system using the compensation method.
The optical phase shifter that constantly rotates the local oscillator phase is a necessity in continuous-variable quantum key distribution systems with heterodyne detection. In previous experimental implementations, the optical phase shifter is generally regarded as an ideal passive optical device that perfectly rotates the phase of the electromagnetic wave of 90 ∘ . However, the optical phase shifter in practice introduces imperfections, mainly the measurement angular error, which inevitably deteriorates the security of the practical systems. Here, we will give a concrete interpretation of measurement angular error in practical systems and the corresponding entanglement-based description. Subsequently, from the parameter estimation, we deduce the overestimated excess noise and the underestimated transmittance, which lead to a reduction in the final secret key rate. Simultaneously, we propose an estimation method of the measurement angular error. Next, the practical security analysis is provided in detail, and the effect of the measurement angular error and its corresponding compensation scheme are demonstrated. We conclude that measurement angular error severely degrades the security, but the proposed calibration and compensation method can significantly help improve the performance of the practical CV-QKD systems.
Continuous variable-quantum key distribution (CV-QKD) based on coherent detection has potential to be a cost-effective solution to deploy secure keys over optical networks. This is due to its compatibility with mature optical communication technologies, such as homodyne and heterodyne detection schemes. Nevertheless, realistic implementations of CV-QKD systems suffer from imperfections in the practical devices used to generate and detect the coherent states. Those imperfections deteriorate the performance of the CV-QKD system and can be exploited by an eavesdropper to steal key information without being detected. In this work, we discuss the impact of practical device imperfections on the excess noise of the CV-QKD and on the achievable transmission distance. We also analyze the impact of detection imperfections on the measurement of the shot noise, and its impact on CV-QKD system security.
Continuous-variable quantum key distribution (CV-QKD) using coherent states and heterodyne detection enables secure quantum communication based on technology that has large similarities to coherent optical telecommunication. Yet, practical implementations of coherent receivers used in both technologies encounter device imperfections, which for CV-QKD are often not addressed in security proofs. Here, we present a theoretical framework that rigorously accounts for imperfect heterodyne measurements arising from phase and amplitude imbalances in the coherent (heterodyne) receiver. Focusing on collective attacks, we establish a finite-size security proof that reveals how measurement imperfections limit the distance over which a positive key rate is achievable. To mitigate these effects, we propose a local transformation during classical post-processing. We validate our approach experimentally on a CV-QKD system with an imperfect coherent receiver, underscoring its potential for scalable, cost-effective CV-QKD with photonic integrated receivers in which phase and amplitude imbalances naturally appear through manufacturing tolerances.
The measurement-device-independent quantum key distribution (MDI-QKD) protocol is immune to imperfect measurement devices. However, its practicality and performance when implemented in continuous-variable (CV) mode are still not satisfactory. We propose a CV-MDI-QKD protocol based on modulated squeezed states, and analyze its security against two-mode Gaussian attack. The results show that the protocol can achieve a higher secret key rate and transmission distance than previous coherent-state and squeezed-state protocols. A method to compensate the imperfection of a practical homodyne detector using phase-sensitive optical amplifiers is also presented. By setting an appropriate optical amplification gain, realistic detectors with ordinary quantum efficiency can be employed. In addition, we discuss the impact of finite-size effects on the secret key rate of the protocol. The methods presented may aid in the practical application of the CV-MDI-QKD protocol.
Continuous-variable quantum key distribution (CV-QKD) enables two remote parties to establish information-theoretically secure keys and offers high practical feasibility due to its compatibility with mature coherent optical communication technologies. However, as CV-QKD systems progress toward digital implementations, device nonidealities drive the optical field from a single-mode to a continuous-mode region, thereby underscoring the mismatch between theoretical models and practical systems. Here, we introduce temporal modes to construct an entanglement-based scheme that more accurately captures device nonidealities and develop a corresponding secret key rate calculation method applicable to continuous-mode scenarios. We demonstrate that optimizing the pulse-shaping format can significantly improve performance under detector-bandwidth-limited conditions. Experimental results also confirm that the proposed model effectively describes the impact of sampling-time deviations. We further analyze a linear weighted-reconstruction digital signal processing method,which improves the secret key rate by approximately 50% in a 30-km fiber experiment without requiring additional hardware, demonstrating a substantial performance enhancement at metropolitan distances. The proposed theoretical framework accommodates a broader range of experimental conditions and can guide the optimization of digital CV-QKD systems.
Phase reference calibration is a necessary procedure in practical continuous-variable measurement-device-independent quantum key distribution (CV-MDI-QKD) for the need of Bell-state measurement. However, the phase reference calibration may become imperfect in practical applications. We explored the practical security of CV-MDI-QKD with imperfect phase reference calibration under realistic conditions of lossy and noisy quantum channels. Specifically, a comprehensive framework is developed to model and characterize the imperfection of the practical phase reference calibration operation, which is mainly caused by the nonsynchronization of two remote lasers in senders. Security analysis shows that the imperfect phase reference calibration has significant side effects on the performance and security of the CV-MDI-QKD protocol. A tight security bound to thermal excess noise introduced by imperfect phase reference calibration is derived for reverse reconciliation against one-mode collective Gaussian attack in the asymptotic limit, and the upper threshold of this imperfection tolerated by the system is obtained. This security analysis framework can eliminate the security hazards caused by imperfect phase reference calibration without changing the existing CV-MDI-QKD system structure. In addition, this work will improve the practical security framework of CV-MDI-QKD protocol and provide theoretic instruction for the experimental implementation of CV-MDI-QKD protocol.