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arXiv:1707.05931 · Physical Review A

Finite-size analysis of continuous-variable measurement-device-independent quantum key distribution

Xueying Zhang, Yichen Zhang, Yijia Zhao, Xiangyu Wang, Song Yu, Hong Mei Guo

Published Oct 25, 2017• 56 citations
arXivHTMLPDF

Abstract

We study the impact of the finite-size effect on the continuous-variable measurement-device-independent quantum key distribution (CV-MDI QKD) protocol, mainly considering the finite-size effect on the parameter estimation procedure. The central-limit theorem and maximum likelihood estimation theorem are used to estimate the parameters. We also analyze the relationship between the number of exchanged signals and the optimal modulation variance in the protocol. It is proved that when Charlie's position is close to Bob, the CV-MDI QKD protocol has the farthest transmission distance in the finite-size scenario. Finally, we discuss the impact of finite-size effects related to the practical detection in the CV-MDI QKD protocol. The overall results indicate that the finite-size effect has a great influence on the secret-key rate of the CV-MDI QKD protocol and should not be ignored.

DOI
10.1103/physreva.96.042334

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We study the impact of the finite-size effect on the continuous-variable measurement-device-independent quantum key distribution (CV-MDI QKD) protocol, mainly considering the finite-size effect on the parameter estimation procedure. The central-limit theorem and maximum likelihood estimation theorem are used to estimate the parameters. We also analyze the relationship between the number of exchanged signals and the optimal modulation variance in the protocol. It is proved that when Charlie's position is close to Bob, the CV-MDI QKD protocol has the farthest transmission distance in the finite-size scenario. Finally, we discuss the impact of finite-size effects related to the practical detection in the CV-MDI QKD protocol. The overall results indicate that the finite-size effect has a great influence on the secret-key rate of the CV-MDI QKD protocol and should not be ignored.
We study the impact of finite-size effects on the key rate of continuous-variable (CV) measurement-device-independent (MDI) quantum key distribution (QKD), considering two-mode Gaussian attacks. Inspired by the parameter estimation technique developed in by Ruppert et al. [Phys. Rev. A 90, 062310 (2014)], we adapt it to study CV-MDI-QKD and, assuming realistic experimental conditions, we analyze the impact of finite-size effects on the key rate. We find that the performance of the protocol approaches the ideal one, increasing the block size, and, most importantly, that blocks between 106{10}^{6}106 and 109{10}^{9}109 data points may provide key rates $\ensuremath{\sim}{10}^{\ensuremath{-}2}$ bit/use over metropolitan distances.
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.
We have introduced, for the first time, a protocol for Continuous-Variable Measurement-Device-Independent Quantum Key Distribution (CV-MDI-QKD) in the terahertz (THz) frequency band. We have conducted a secret key rate analysis against collective attacks. The proposed THz CV-MDI-QKD is immune to all detector attacks, significantly enhancing the security assurance of practical THz CVQKD implementations. Furthermore, we investigated the impact of finite key length (the finite-size effect) and finite reconciliation efficiency on the performance of practical THz CV-MDI-QKD systems. Our findings reveal that by employing a large number of keys or signals and optimizing the modulation variance, the detrimental effects arising from the finite-size effect and suboptimal reconciliation efficiency can be notably mitigated. These insights play a crucial role in advancing the feasibility of THz CVQKD technology towards practical applications.
We present a rigorous security analysis of continuous-variable measurement-device-independent quantum key distribution (CV MDI QKD) in a finite-size scenario. The security proof is obtained in two steps: by first assessing the security against collective Gaussian attacks, and then extending to the most general class of coherent attacks via the Gaussian de Finetti reduction. Our result combines recent state-of-the-art security proofs for CV QKD with findings about min-entropy calculus and parameter estimation. In doing so, we improve the finite-size estimate of the secret key rate. Our conclusions confirm that CV MDI protocols allow for high rates on the metropolitan scale, and may achieve a nonzero secret key rate against the most general class of coherent attacks after 107{10}^{7}107--109{10}^{9}109 quantum signal transmissions, depending on loss and noise, and on the required level of security.
Continuous-variable measure-device-independent quantum key distribution (CV-MDI QKD) is proposed to remove all imperfections originating from detection. However, there are still some inevitable imperfections in a practical CV-MDI QKD system. For example, there is a fluctuating channel transmittance in the complex communication environments. Here we investigate the security of the system under the effects of the fluctuating channel transmittance, where the transmittance is regarded as a fixed value related to communication distance in theory. We first discuss the parameter estimation in fluctuating channel transmittance based on these establishing of channel models, which has an obvious deviation compared with the estimated parameters in the ideal case. Then, we show the evaluated results when the channel transmittance respectively obeys the two-point distribution and the uniform distribution. In particular, the two distributions can be easily realized under the manipulation of eavesdroppers. Finally, we analyze the secret key rate of the system when the channel transmittance obeys the above distributions. The simulation analysis indicates that a slight fluctuation of the channel transmittance may seriously reduce the performance of the system, especially in the extreme asymmetric case. Furthermore, the communication between Alice, Bob and Charlie may be immediately interrupted. Therefore, eavesdroppers can manipulate the channel transmittance to complete a denial-of-service attack in a practical CV-MDI QKD system. To resist this attack, the Gaussian post-selection method can be exploited to calibrate the parameter estimation to reduce the deterioration of performance of the system.
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.