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arXiv:2406.14610 · Optica

Composable continuous-variable multi-user QKD with discrete modulation: theory and implementation

Florian Kanitschar, Adnan A. E. Hajomer, Michael Hentschel, Tobias Gehring, Christoph Pacher

Published Jun 29, 2026• 0 citations
arXivHTMLPDF

Abstract

Establishing scalable, secure quantum networks requires advancing beyond conventional point-to-point quantum key distribution (QKD) protocols toward point-to-multipoint QKD protocols. Here, we generalize a well-established discrete-modulated continuous-variable (CV) QKD protocol from the point-to-point to the point-to-multipoint setting. We present a comprehensive security analysis across different scenarios and derive secret key rates for loss-only and noisy channels, both in the asymptotic and the composable finite-size regime. Experimentally, we validate the protocol in a passive optical network with 10 km access links, achieving a composable secure key rate of 2.185×10 −3 bits per symbol (0.273 Mbit/s) against independent and identically distributed collective attacks. Our results demonstrate that discrete-modulated CV-QKD can support access networks with multiple users while relying solely on cost-efficient, off-the-shelf telecommunication components, paving the way toward practical, scalable, and secure quantum networks.

DOI
10.1364/optica.588301

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Abstract Establishing secure data communication necessitates secure key exchange over a public channel. Quantum key distribution (QKD), which leverages the principles of quantum physics, can achieve this with information-theoretic security. The discrete modulated (DM) continuous variable (CV) QKD protocol, in particular, is a suitable candidate for large-scale deployment of quantum-safe communication due to its simplicity and compatibility with standard high-speed telecommunication technology. Here, we present the first experimental demonstration of a four-state DM CVQKD system, successfully generating composable finite-size keys, secure against collective attacks over a 20 km fiber channel with 2.3 × 109 coherent quantum states, achieving a positive composable key rate of 11.04 × 10−3 bits/symbol. This accomplishment is enabled by using an advanced security proof, meticulously selecting its parameters, and the fast, stable operation of the system. Our results mark a significant step toward the large-scale deployment of practical, high-performance, cost-effective, and highly secure quantum key distribution networks using standard telecommunication components.
In recent years, continuous-variable quantum key distribution (CV-QKD) has become a promising paradigm for enabling secure communication among multiple end users sharing the same telecommunication backbone. CV-QKD with reverse reconciliation naturally enables scalability from conventional point-to-point links to quantum access networks based on passive quantum broadcasting channels. Here, we report an experimental demonstration on an active 1:41:41:4 multi-user CV quantum network (QN) in the finite-size regime. With 1.25⋅1091.25\cdot10^91.25⋅109 coherent states exchanged on each 11km11\text{km}11km quantum channel, the highest performance for secret key generation totaling 1.9⋅10−11.9\cdot10^{-1}1.9⋅10−1 bits/channel use. Furthermore, we investigate adaptable CV-QN protocols that comprehensively allow network operation in various security and key rates requirements of individual users. The results establish the practical security of CV-QN compatible with existing telecommunication for broad deployment, and allowing additional degree of freedom for connected end users in existing infrastructures.
Continuous-variable (CV) quantum key distribution (QKD) allows for quantum secure communication with the benefit of being close to classical coherent communication. In recent years, CV QKD protocols using a discrete number of displaced coherent states have been studied intensively as the modulation can be directly implemented with real devices with finite resolution. Until now, experiments only calculated key rates in the asymptotic regime. Here, we present a CV QKD system using discrete modulation that is especially designed for atmospheric channels. We use polarization encoding to exploit the nonbirefringent nature of the turbulent atmosphere. This allows to expand CV QKD networks beyond the existing fiber backbone. In a laboratory demonstration with a static 3-decibel loss channel, we implemented a recently developed security proof allowing to calculate composable finite-size key rates against independently and identically distributed collective attacks. We applied the full QKD protocol including a quantum random number generator, error correction, and privacy amplification to extract secret keys.
Discrete-Modulated (DM) Continuous-Variable (CV) Quantum Key Distribution (QKD) is an experimentally attractive approach to quantum cryptography, offering high key rates over metropolitan-scale distances while relying on state-of-the-art telecom infrastructure. However, a fundamental gap has remained between this experimental promise and rigorous security: for more than two decades, DM CV-QKD has lacked a complete composable finite-size security proof against coherent attacks. Existing works either restrict the adversary to collective attacks, impose additional finite-dimensional assumptions, apply only to specific modulation formats, or fail to recover the known asymptotic rates. Here, we resolve this longstanding problem by establishing the first complete composable finite-size security proof for DM CV-QKD protocols against coherent attacks, incorporating imperfect detectors and both fixed- and variable-length protocol variants. Our proof introduces two central results of broader interest: an infinite-dimensional marginal-constrained entropy accumulation theorem (iMEAT) and a rigorous dimension-reduction technique that makes the infinite-dimensional security bounds numerically tractable. The resulting key rates recover the known asymptotic rates and outperform established finite-size bounds based on collective attacks, while yielding positive key rates beyond 707070km for experimentally relevant block sizes and parameters. Thus, our work closes a longstanding gap and places an experimentally attractive class of CV-QKD protocols on a rigorous composable security footing and provides a pathway towards their practical deployment.
Continuous variable (CV) quantum key distribution (QKD) provides a powerful setting for secure quantum communications, thanks to the use of room-temperature off-the-shelf optical devices and the potential to reach much higher rates than the standard discrete-variable counterpart. In this paper, we provide a general framework for studying the composable finite-size security of CV-QKD with Gaussian-modulated coherent-state protocols under various levels of trust for the loss and noise experienced by the parties. Our paper considers both wired (i.e., fiber-based) and wireless (i.e., free-space) quantum communications. In the latter case, we show that high key rates are achievable for short-range optical wireless (LiFi) in secure quantum networks with both fixed and mobile devices. Finally, we extend our investigation to microwave wireless (WiFi) discussing security and feasibility of CV-QKD for very short-range applications.
To establish a scalable and secure quantum network, a critical milestone is advancing from basic point-to-point quantum key distribution (QKD) systems to the development of inherently multi-user protocols designed to maximize network capacity. Here, we propose a quantum passive optical network (QPON) protocol based on continuous-variable (CV) systems, particularly the quadrature of the coherent state, which enables deterministic, simultaneous, and high-rate secret key generation among all network users. We implement two protocols with different trust levels assigned to the network users and experimentally demonstrate key generation in a quantum access network with 8 users, each with an 11 km span of access link. Depending on the trust assumptions about the users, we reach 1.5 and 2.1 Mbits/s of total network key generation (or 0.4 and 1.0 Mbits/s with finite-size channels estimation). Demonstrating the potential to expand the network's capacity to accommodate tens of users at a high rate, our CV-QPON protocols open up new possibilities in establishing low-cost, high-rate, and scalable secure quantum access networks serving as a stepping stone towards a quantum internet.