Composable free-space continuous-variable quantum key distribution using discrete modulation
Kevin Jaksch, Thomas Dirmeier, Yannick Weiser, Stefan Richter, Ömer Bayraktar, Bastian Hacker, Conrad Rößler, Imran Khan, Stefan Petscharnig, Thomas Alexander Grafenauer, Michael Hentschel, Bernhard Ömer, Christoph Pacher, Florian Kanitschar, Twesh Upadhyaya, Jie Lin, Norbert Lütkenhaus, Gerd Leuchs, Christoph Marquardt
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.
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.
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.
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.
Discrete-modulated (DM) continuous-variable quantum key distribution (CV-QKD) protocols are promising candidates for commercial implementations of quantum communication networks due to their experimental simplicity.While tight security analyses in the asymptotic limit exist, proofs in the finitesize regime are still subject to active research.We present a composable finite-size security proof against independently and identically distributed collective attacks for a general DM CV-QKD protocol.We introduce a new energy testing theorem to bound the effective dimension of Bob's system and rigorously prove security within Renner's -security framework and address the issue of acceptance sets in protocols and their security proof.We want to highlight that our method also allows for nonunique acceptance statistics, which is necessary in practise.Finally, we extend and apply a numerical security proof technique to calculate tight lower bounds on the secure key rate.To demonstrate our method, we apply it to a quadrature phase-shift keying protocol for both untrusted, ideal and trusted, nonideal detectors.The results show that our security proof method yields secure finite-size key rates under experimentally viable conditions up to at least 72 km transmission distance.
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 70km 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.
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.
We consider discrete-modulation protocols for continuous-variable quantum key distribution (CV-QKD) that employ a modulation constellation consisting of a finite number of coherent states and that use a homodyne- or a heterodyne-detection receiver. We establish a security proof for collective attacks in the asymptotic regime, and we provide a formula for an achievable secret-key rate. Previous works established security proofs for discrete-modulation CV-QKD protocols that use two or three coherent states. The main constituents of our approach include approximating a complex, isotropic Gaussian probability distribution by a finite-size Gauss-Hermite constellation, applying entropic continuity bounds, and leveraging previous security proofs for Gaussian-modulation protocols. As an application of our method, we calculate secret-key rates achievable over a lossy thermal bosonic channel. We show that the rates for discrete-modulation protocols approach the rates achieved by a Gaussian-modulation protocol as the constellation size is increased. For pure-loss channels, our results indicate that in the high-loss regime and for sufficiently large constellation size, the achievable key rates scale optimally, i.e., proportional to the channel's transmissivity.