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Entropy

Performance Improvement for Discretely Modulated Continuous-Variable Measurement-Device-Independent Quantum Key Distribution with Imbalanced Modulation

Zehui Liu, Jiandong Bai, Fengchao Li, Yijun Li, Yan Tian, Wenyuan Liu

Published Feb 3, 2025• 0 citations
Publisher

Abstract

The modulation mode at the transmitters plays a crucial role in the continuous-variable measurement-device-independent quantum key distribution (CV-MDI-QKD) protocol. However, in practical applications, differences in the modulation schemes between two transmitters can inevitably impact protocol performance, particularly when using discrete modulation with four-state or eight-state formats. This work primarily investigates the effect of imbalanced modulation at the transmitters on the security of the CV-MDI-QKD protocol under both symmetric and asymmetric distance scenarios. By employing imbalanced discrete modulation maps and numerical convex optimization techniques, the proposed CV-MDI-QKD protocol achieves a notably higher secret key rate and outperforms existing protocols in terms of maximum transmission distance. Specifically, simulation results demonstrate that the secret key rate and maximum transmission distance are boosted by approximately 77.77% and 24.3%, respectively, compared to the original protocol. This novel and simplified modulation method can be seamlessly implemented in existing experimental setups without requiring equipment modifications. Furthermore, it provides a practical approach to enhancing protocol performance and enabling cost-effective applications in secure quantum communication networks under real-world environments.

DOI
10.3390/e27020160

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The modulation mode at the transmitters plays a crucial role in the continuous-variable measurement-device-independent quantum key distribution (CV-MDI-QKD) protocol. However, in practical applications, differences in the modulation schemes between two transmitters can inevitably impact protocol performance, particularly when using discrete modulation with four-state or eight-state formats. This work primarily investigates the effect of imbalanced modulation at the transmitters on the security of the CV-MDI-QKD protocol under both symmetric and asymmetric distance scenarios. By employing imbalanced discrete modulation maps and numerical convex optimization techniques, the proposed CV-MDI-QKD protocol achieves a notably higher secret key rate and outperforms existing protocols in terms of maximum transmission distance. Specifically, simulation results demonstrate that the secret key rate and maximum transmission distance are boosted by approximately 77.77% and 24.3%, respectively, compared to the original protocol. This novel and simplified modulation method can be seamlessly implemented in existing experimental setups without requiring equipment modifications. Furthermore, it provides a practical approach to enhancing protocol performance and enabling cost-effective applications in secure quantum communication networks under real-world environments.
Continuous variable measurement-device-independent quantum key distribution (CV-MDI-QKD) removes all known or unknown side-channel attacks on detectors. However, it is difficult to fully implement assumptions in the security demonstration model, which leads to potential security vulnerabilities inevitably existing in the practical system. In this paper, we explore the impact of imbalanced modulation at transmitters on the security of the CV-MDI-QKD system mainly using a coherent state and squeezed state under symmetric and asymmetric distances. Assuming two different modulation topologies of senders, we propose a generalized theoretical scheme and evaluate the key parameter achievable of the protocol with the mechanism of imbalanced modulation. The presented results show that imbalanced modulation can achieve a relatively nonlinearly higher secret key rate and transmission distances than the previous protocol which is the balanced modulation variance used by transmitters. The advantage of imbalanced modulation is demonstrated for the system key parameter estimation using numerical simulation under different situations. In addition, the consequences indicate the importance of imbalanced modulation on the performance of CV-MDI-QKD protocol and provide a theoretical framework for experimental implementation as well as the optimal modulated mode.
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.
Abstract Discrete modulation can make up for the shortage of transmission distance in measurement-device-independent continuous-variable quantum key distribution (MDI-CVQKD), providing a unique advantage against all side-channel attacks but also creating a challenge for further performance improvement. Here we suggest a quantum catalysis (QC) approach for enhancing the performance of the discrete-modulated (DM) MDI-CVQKD in terms of the achievable secret key rate and lengthening the maximal transmission distance. The numerical simulation results show that the QC-based MDI-CVQKD with discrete modulation, involving a zero-photon catalysis (ZPC) operation, can not only obtain a higher secret key rate than the original DM protocol, but also contribute to a reasonable increase of the corresponding optimal variance. As for the extreme asymmetric and symmetric cases, the secret key rate and maximal transmission distance of the ZPC-involved DM MDI-CVQKD system can be further improved under the same parameters. This approach enables the system to tolerate lower reconciliation efficiency, which may provide excellent potential for practical implementations with state-of-art technology.
We propose a long-distance continuous-variable measurement-device-independent quantum key distribution (CV-MDI-QKD) protocol with discrete modulation. This kind of discrete-modulated scheme has good compatibility with efficient error correction code, which leads to higher reconciliation efficiency even at low signal-to-noise ratio. Security analysis shows that the proposed protocol is secure against arbitrary collective attacks in the asymptotic limit with the proper use of decoy states. With the use of discrete modulation, the proposed CV-MDI-QKD protocol has simpler implementation and outperforms previous protocols in terms of achievable maximal transmission distance, which precisely solved the bottleneck of the original Gaussian-modulated CV-MDI-QKD protocol.
Continuous-variable measurement-device-independent quantum key distribution (CV-MDI-QKD) allows remote parties to share information-theoretical secure keys while defending all the side-channel attacks on measurement devices. However, the secure transmission distance and the secret key rate are quite limited due to the high untrusted equivalent excess noise in the Gaussian modulation. More particularly, extremely high-efficiency homodyne detections are required for even non-zero secure transmission distances, which directly restrict its practical realization. Here, we propose a CV-MDI-QKD protocol by encoding the key information into matched discrete phases of two groups of coherent states, which decreases the required detection efficiency for ideally asymmetric cases, and makes it possible to practically achieve secure key distribution with current low-efficiency homodyne detections. Besides, a proof-of-principle experiment with a locally generated oscillator is implemented, which, for the first time, demonstrates the realizability of CV-MDI-QKD using all fiber-based devices. The discrete-modulated phase-matching method provides an alternative direction of an applicable quantum key distribution with practical security.
Continuous-variable measurement-device-independent quantum key distribution (CV-MDI QKD) can address vulnerabilities on the detection side of a QKD system. The core of this protocol involves continuous-variable Bell measurements performed by an untrusted third party. However, in high-speed systems, spectrum broadening causes Bell measurements to deviate from the ideal single-mode scenario, resulting in mode mismatches, reduced performance, and compromised security. Here, we introduce temporal modes (TMs) to analyze the performance of CV-MDI QKD under continuous-mode scenarios. The mismatch between Bob's transmitting mode and Bell measurement mode has a more significant effect on system performance compared to that on Alice's side. When the Bell receiver is close to Bob and the mismatch is set to just 5%, the transmission distance drastically decreases from 87.96 km to 18.50 km. In comparison, the same mismatch for Alice reduces the distance to 86.83 km. This greater degradation on Bob's side can be attributed to the asymmetry in the data modification step. Furthermore, the mismatch in TM characteristics leads to a significant reduction in the secret key rate by 83% when the transmission distance is set to 15 km, which severely limits the practical usability of the protocol over specific distances. These results indicate that in scenarios involving continuous-mode interference, such as large-scale MDI network setups, careful consideration of each user's TM characteristics is crucial. Rigorous pre-calibration of these modes is essential to ensure the system's reliability and efficiency.