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Chinese Physics B

Finite-size analysis of eight-state continuous-variable quantum key distribution with the linear optics cloning machine

Hang Zhang, Yu Mao, Duan Huang, Ying Guo, Xiaodong Wu, Ling Zhang

Published Sep 1, 2018• 12 citations
Publisher

Abstract

We propose a method to improve the secret key rate of an eight-state continuous-variable quantum key distribution (CVQKD) by using a linear optics cloning machine (LOCM). In the proposed scheme, an LOCM is exploited to compensate for the imperfections of Bob's apparatus, so that the generated secret key rate of the eight-state protocol could be well enhanced. We investigate the security of our proposed protocol in a finite-size scenario so as to further approach the practical value of a secret key rate. Numeric simulation shows that the LOCM with reasonable tuning gain λ and transmittance τ can effectively improve the secret key rate of eight-state CVQKD in both an asymptotic limit and a finite-size regime. Furthermore, we obtain the tightest bound of the secure distance by taking the finite-size effect into account, which is more practical than that obtained in the asymptotic limit.

DOI
10.1088/1674-1056/27/9/090307

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We propose a method to improve the secret key rate of an eight-state continuous-variable quantum key distribution (CVQKD) by using a linear optics cloning machine (LOCM). In the proposed scheme, an LOCM is exploited to compensate for the imperfections of Bob's apparatus, so that the generated secret key rate of the eight-state protocol could be well enhanced. We investigate the security of our proposed protocol in a finite-size scenario so as to further approach the practical value of a secret key rate. Numeric simulation shows that the LOCM with reasonable tuning gain λ and transmittance τ can effectively improve the secret key rate of eight-state CVQKD in both an asymptotic limit and a finite-size regime. Furthermore, we obtain the tightest bound of the secure distance by taking the finite-size effect into account, which is more practical than that obtained in the asymptotic limit.
In experimental setups of continuous-variable quantum key distribution (CVQKD) independently modulating the amplitude and phase of coherent states, the ideal Gaussian modulation will be degraded into discretized polar modulation (DPM) due to the finite resolution of the driving voltages of electro-optical modulators. To compensate for the performance degradation induced by the joint effect of amplitude and phase discretization, linear optics cloning machine (LOCM) can be introduced on the receiver side. Implemented by linear optical elements, heterodyne detection and controlled displacement, LOCM introduces extra noise that can be transformed into an advantageous one to combat channel excess noise by dynamically adjusting the relevant parameters into a suitable range. In this paper, the prepare-and-measure version of LOCM DPM-CVQKD is presented, where the incoming signal state enters a tunable LOCM before being measured by the nonideal heterodyne detector. The equivalent entanglement-based model is also established to perform security analysis, where the LOCM is reformulated into combination of the incoming signal state and a thermal state on a beam splitter. The composable secret key rate is derived to investigate the security of LOCM DPM-CVQKD. Simulation results demonstrate that the composable secret key rate and transmission distance are closely related to the tuning gain and the transmittance of LOCM. Once these two parameters are set to appropriate values, LOCM can improve the secret key rate and transmission distance of DPM-CVQKD, as well as its resistance to excess noise. Meanwhile, taking finite-size effect into consideration, the LOCM can also effectively reduce the requirement for the block size of the exchanged signals, which is beneficial to the feasibility and practicability of CVQKD. Owing to the fact that the performance of LOCM DPM-CVQKD is largely reliant on the calibration selection of relevant parameters, further research may concentrate on the optimization of LOCM in experimental implementations, where machine learning related methods may be utilized.
We show that the secret key generation rate can be balanced with the maximum secure distance of four-state continuous-variable quantum key distribution (CV-QKD) by using the linear optics cloning machine (LOCM). Benefiting from the LOCM operation, the LOCM-tuned noise can be employed by the reference partner of reconciliation to achieve higher secret key generation rates over a long distance. Simulation results show that the LOCM operation can flexibly regulate the secret key generation rate and the maximum secure distance and improve the performance of four-state CV-QKD protocol by dynamically tuning parameters in an appropriate range.
We show that the tolerable excess noise can be elegantly controlled while inserting a tunable linear optics cloning machine (LOCM) for continuous-variable key distribution (CVQKD). The LOCM-tuned noise can be stabilized to an optimal value by the reference partner of reconciliation to guarantee the high secret key rate. Simulation results show that there is a considerable improvement of the performance for the LOCM-based CVQKD protocol in terms of the secret rate while making a fine balance between the secret key rate and the transmission distance with the dynamically tuned parameters in suitable ranges.
In experimental setups of continuous-variable quantum key distribution (CVQKD) independently modulating the amplitude and phase of coherent states, the ideal Gaussian modulation will be degraded into discretized polar modulation (DPM) due to the finite resolution of the driving voltages of electro-optical modulators. To compensate for the performance degradation induced by the joint effect of amplitude and phase discretization, linear optics cloning machine (LOCM) can be introduced at the receiver side to reduce the impact of channel excess noise. Implemented by linear optical elements, homodyne detection and controlled displacement, LOCM introduces extra noise that can be transformed into an advantageous one to combat channel excess noise by dynamically adjusting the relevant parameters into a suitable range. In this paper, the prepare-and-measure version of LOCM DPM-CVQKD is presented, where the incoming signal state enters a tunable LOCM before being measured by the nonideal heterodyne detector. The equivalent entanglement-based model is also established to perform security analysis, where the LOCM is reformulated into combining the incoming signal state and a thermal state on a beam splitter. The composable secret key rate is derived to investigate the security of LOCM DPM-CVQKD. Simulation results demonstrate that the secret key rate is closely related to the tuning gain and the transmittance of LOCM. Once the two parameters are set to appropriate values, LOCM allows the promotion of the secret key rate of DPM-CVQKD, as well as its resistance to excess noise. Meanwhile, taking finite-size effect into consideration, LOCM can also effectively reduce the requirement for the block size of the exchanged signals, which is beneficial to the feasibility and practicability of CVQKD. Since the performance of LOCM DPM-CVQKD is heavily reliant on the calibrate selection of relevant parameters, further research may concentrate on the optimization of LOCM in experimental implementations, where machine learning related methods may be exploited.
Continuous-variable quantum key distribution (CVQKD) protocols with entanglement in the middle (EM) enable long maximal transmission distances for quantum communications. For the security analysis of the protocols, it is usually assumed that Eve performs collective Gaussian attacks and there is a lack of finite-size analysis of the protocols. However, in this paper we consider the finite-size regime of the EM-based CVQKD protocols by exposing the protocol to collective attacks and coherent attacks. We differentiate between the collective attacks and the coherent attacks while comparing asymptotic key rate and the key rate in the finite-size scenarios. Moreover, both symmetric and asymmetric configurations are collated in a contrastive analysis. As expected, the derived results in the finite-size scenarios are less useful than those acquired in the asymptotic regime. Nevertheless, we find that CVQKD with entanglement in the middle is capable of providing fully secure secret keys taking the finite-size effects into account with transmission distances of more than 30 km.
The security of the linear optics cloning machine-enhanced passive continuous-variable measurement-device-independent quantum key distribution is investigated. Passive state preparation is employed at both legitimate parties to reduce the system complexity and eliminate the strict requirements on electro-optical modulators. At the receiver, linear optics cloning machine is utilized to compensate for the degradation induced by the preparation noise. In the presence of detection noise, the expression of the composable secret key rate of the proposed scheme under collective attacks is derived, and simulation results show that the proposed scheme can flexibly optimize the system performance under both symmetric scheme and asymmetric scheme.