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Chinese Physics B

Finite-size analysis of continuous-variable quantum key distribution with entanglement in the middle

Ying Guo, Yu Su, Jian Zhou, Ling Zhang, Duan Huang

Published Jan 1, 2019• 10 citations
Publisher

Abstract

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.

DOI
10.1088/1674-1056/28/1/010305

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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 Gaussian-modulated continuous-variable quantum key distribution (GMCVQKD) scheme based on untrusted entanglement sources simulates scenarios where the source may be controlled by an attacker. However, Existing analyses often assume ideal settings and overlook finite-size effects. This paper addresses these gaps by evaluating the GMCVQKD scheme under specific attack scenarios, considering limited signal exchanges between Alice and Bob. We examine the secret key rate under finite-size conditions, analyzing factors such as the positioning of the entanglement source and the effectiveness of the reconciliation process., and compares results to the asymptotic regime. The findings reveal a decline in key rate under finite-size effects, highlighting the influence of statistical fluctuations. This work advances practical CVQKD implementation and offers theoretical guidance for system deployment.
The goal of this paper is to extend the framework of finite-size analysis recently developed for quantum key distribution to continuous-variable protocols. We do not solve this problem completely here, and we mainly consider the finite-size effects on the parameter estimation procedure. Despite the fact that some questions are left open, we are able to give an estimation of the secret key rate for protocols which do not contain a postselection procedure. As expected, these results are significantly more pessimistic than those obtained in the asymptotic regime. However, we show that recent continuous-variable protocols are able to provide fully secure secret keys in the finite-size scenario, over distances larger than 505050 km.
A modified continuous-variable quantum key distribution (CVQKD) protocol is proposed by originating the entangled source from a malicious third party Eve in the middle instead of generating it from the trustworthy Alice or Bob. This method is able to enhance the efficiency of the CVQKD scheme attacked by local oscillator (LO) intensity attack in terms of the generated secret key rate in quantum communication. The other indication of the improvement is that the maximum transmission distance and the maximum loss tolerance can be increased significantly, especially for CVQKD schemes based on homodyne detection.
We conducted a study to evaluate the performance of Terahertz Continuous Variable Quantum Key Distribution (THz CVQKD) systems in atmospheric conditions with the finite-size effect. Our research delved into the secure key rates and transmission distances of THz CVQKD for four protocols, all based on Gaussian coherent states, under the threat of collective Gaussian attacks. These protocols include reverse reconciliation with homodyne detection, direct reconciliation with homodyne detection, reverse reconciliation with heterodyne detection, and direct reconciliation with heterodyne detection. Our findings revealed distinctive key rates across various THz frequencies and protocols. However, the finite-size effect had a diminishing impact on the key rates of CVQKD in all scenarios. Fortunately, by harnessing a substantial number of keys exceeding 1012 and optimizing modulation variance, both the key rates and transmission distances of THz CVQKD can be significantly extended. This research contributes to advancing the practicality of THz CVQKD technology.
We perform security analysis of a passive continuous-variable quantum key distribution (CV-QKD) protocol by considering the finite-size effect. In the passive CV-QKD scheme, Alice utilizes thermal sources to passively make preparation of quantum state without Gaussian modulations. With this technique, the quantum states can be prepared precisely to match the high transmission rate. Here, both asymptotic regime and finite-size regime are considered to make a comparison. In the finite-size scenario, we illustrate the passive CV-QKD protocol against collective attacks. Simulation results show that the performance of passive CV-QKD protocol in the finite-size case is more pessimistic than that achieved in the asymptotic case, which indicates that the finite-size effect has a great influence on the performance of the single-mode passive CV-QKD protocol. However, we can still obtain a reasonable performance in the finite-size regime by enhancing the average photon number of the thermal state.
The discretely modulated continuous-variable quantum key distribution (DM CVQKD) has been proven to be secure, and a basic assumption for the current theoretical security proof of the DM CVQKD is that the signal source cannot be compromised. However, this assumption is quite unpractical in real quantum communication systems. In this paper, we investigate the DM CVQKD with a special configuration in which the entanglement source is placed at the untrusted channel. With this configuration, the source is no longer protected by the sender but is exposed to the vulnerable environment. In particular, we consider the configuration for two typical DM CVQKD protocols, which are the four-state protocol and the eight-state protocol. Security analysis based on linear bosonic channel shows that the DM CVQKD with an untrusted entanglement source is able to defend itself against the most powerful quantum collective attack in a certain distance range and it can still generate positive secret key rate when considering finite-size effect and composable security, thereby providing a theoretical proof for applying the DM CVQKD system to a realistic environment.