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Frontiers in Quantum Science and Technology

Theoretical development of discrete-modulated continuous-variable quantum key distribution

Wen‐Bo Liu, Chenlong Li, Zhiping Liu, Min-Gang Zhou, Hua‐Lei Yin, Zeng‐Bing Chen

Published Oct 13, 2022• 8 citations
Publisher

Abstract

Continuous-variable quantum key distribution offers simple, stable and easy-to-implement key distribution systems. The discrete modulation scheme further reduces the technical difficulty. The main regret is that the security of discrete modulation schemes has not been sufficiently demonstrated. Schemes with different signal state distributions use various physical conditions to obtain the key rate formula, resulting in different security levels, computation complexities and implementation difficulties. Therefore, a relatively systematic and logically consistent security proof against most general attacks is worth exploring. On the other hand, extending the discrete modulation scheme and its variants to different applications, such as satellite-to-earth communication, can further activate and advance this field. Here, we briefly review the achievements that have been made in discrete-modulated continuous-variable quantum key distribution, and openly discuss some issues worthy of further research.

DOI
10.3389/frqst.2022.985276

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Continuous-variable quantum key distribution offers simple, stable and easy-to-implement key distribution systems. The discrete modulation scheme further reduces the technical difficulty. The main regret is that the security of discrete modulation schemes has not been sufficiently demonstrated. Schemes with different signal state distributions use various physical conditions to obtain the key rate formula, resulting in different security levels, computation complexities and implementation difficulties. Therefore, a relatively systematic and logically consistent security proof against most general attacks is worth exploring. On the other hand, extending the discrete modulation scheme and its variants to different applications, such as satellite-to-earth communication, can further activate and advance this field. Here, we briefly review the achievements that have been made in discrete-modulated continuous-variable quantum key distribution, and openly discuss some issues worthy of further research.
Continuous-variable quantum key distribution (CV-QKD) has emerged as a promising approach for secure quantum communication, offering advantages such as high key generation rates, compatibility with standard telecommunication infrastructure, and potential for integration on photonic chips. This review provides an accessible introduction to the theory of CV-QKD, aimed at researchers entering this rapidly developing field. We focus on fundamental concepts, key protocols, and security analysis essential for understanding CV-QKD systems, with a special emphasis on prepare-and-measure protocols using coherent states under asymptotic security conditions. We explain their equivalence to entanglement-based protocols and detail the security proof framework against collective attacks, encompassing both Gaussian and discrete modulation schemes. We also briefly address more advanced topics, including measurement-device-independent CV-QKD and finite-size security analysis. This work is motivated by Brazil's growing investment in quantum communication technologies. By presenting a clear learning path from basic concepts to advanced topics, this work aims to equip newcomers with the essential tools to engage with current research in CV-QKD, thereby supporting the training of a new generation of researchers in this strategic field.
The key features of continuous variables quantum key distribution protocols are considered in the paper. The motivation for studying and developing methods of quantum cryptography is substantiated. The main aspects inherent to continuous-variable protocols are highlighted, and they are classified based on various characteristics, peculiarities, and implementation variants. A detailed examination of a protocol example with discrete modulation and signal registration through balanced homodyne detection is provided. A classification of attacks on the quantum protocol is presented. A general overview of post-processing methods is given. The role of noise is indicated, and approaches to assessing the level of security applicable to continuous-variable protocols are discussed. In conclusion, the main conclusions regarding the current status of this problem are presented, and aspects requiring further study are identified.
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Quantum key distribution provides secure keys with information-theoretic security ensured by the principle of quantum mechanics. The continuous-variable version of quantum key distribution using coherent states offers the advantages of its compatibility with telecom industry, e.g., using commercial laser and homodyne detector, is now going through a booming period. In this review article, we describe the principle of continuous-variable quantum key distribution system; focus on protocols based on coherent states, whose systems are gradually moving from proof-of-principle lab demonstrations to in-field implementations and technological prototypes. We start by reviewing the theoretical protocols and the current security status of these protocols. Then, we discuss the system structure, the key module, and the mainstream system implementations. The advanced progresses for future applications are discussed, including the digital techniques, system on chip, and point-to-multipoint system. Finally, we discuss the practical security of the system and conclude with promising perspectives in this research field.
Continuous variable quantum key distribution via discrete modulations ensures information-theoretic security using standard telecom technologies, providing affordable and scalable quantum communications with simplified classical postprocessing. However, existing security proofs against general attacks often rely on restrictive assumptions, such as a bounded dimension for coherent states, or require impractically large block sizes. In this work, we develop a finite-size security analysis that removes these limitations while incorporating realistic experimental features. Our approach combines an optimization under infinite dimensions, a security proof against general attacks, a trusted detector model accounting for the receiver imperfections, and postselection strategies to reuse discarded measurement outcomes. We report positive key rates in the finite-size regime for relevant block sizes of the order of 10710^7107. These results contribute to narrowing the gap between theoretical security proofs and practical implementations of discrete-modulated continuous variable quantum key distribution protocols.
Abstract Satellite‐to‐ground quantum communication constitutes the cornerstone of the global quantum network, heralding the advent of the future of quantum information. Continuous‐variable quantum key distribution is a strong candidate for the space‐ground quantum communication due to its simplicity, stability, and ease of implementation, especially for the robustness of space background light noise. Recently, the discrete‐modulated continuous‐variable protocol has garnered increased attention, owing to its lower implementation requirements, acceptable security key rate, and pronounced compatibility with extant infrastructures. Here, key rates are derived for discrete‐modulated continuous‐variable quantum key distribution protocols in free‐space channel environments across various conditions through numerical simulation, revealing the viability of its application in satellite‐to‐ground communication.