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arXiv:2504.06384 · Physical Review A

Continuous-variable quantum key distribution with composable security and tight error-correction bound towards constrained-device implementations

Anonymous, Carlo Ottaviani, Stefano Pirandola, Poonam Yadav, Marco Lucamarini

Published Jul 13, 2026• 0 citations
arXivHTMLPDF

Abstract

Constrained devices, such as smart sensors, wearable devices, and Internet of Things nodes, are increasingly prevalent in society and rely on secure communications to function properly. These devices often operate autonomously, exchanging sensitive data or commands over short distances, such as within a room, house, or warehouse. In this context, continuous-variable quantum key distribution (CV-QKD) offers the highest secure key rate and the greatest versatility for integration into existing infrastructure. A key challenge in this setting, where devices have limited storage and processing capacity, is obtaining a realistic and tight estimate of the CV-QKD secure key rate within a composable security framework, with error correction (EC) consuming most of the storage and computational power. To address this, we focus on low-density parity-check codes with nonbinary alphabets, which optimize mutual information and are particularly suited for short-distance communications. We develop a security framework to derive finite-size secret keys near the optimal EC leakage limit and model the related memory requirements for the encoding process in one-way error correction. This analysis facilitates the practical deployment of CV-QKD, particularly in constrained devices with limited storage and computational resources.

DOI
10.1103/2s9n-s2br

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Constrained devices, such as smart sensors, wearable devices, and Internet of Things nodes, are increasingly prevalent in society and rely on secure communications to function properly. These devices often operate autonomously, exchanging sensitive data or commands over short distances, such as within a room, house, or warehouse. In this context, continuous-variable quantum key distribution (CV-QKD) offers the highest secure key rate and the greatest versatility for integration into existing infrastructure. A key challenge in this setting, where devices have limited storage and processing capacity, is obtaining a realistic and tight estimate of the CV-QKD secure key rate within a composable security framework, with error correction (EC) consuming most of the storage and computational power. To address this, we focus on low-density parity-check codes with nonbinary alphabets, which optimize mutual information and are particularly suited for short-distance communications. We develop a security framework to derive finite-size secret keys near the optimal EC leakage limit and model the related memory requirements for the encoding process in one-way error correction. This analysis facilitates the practical deployment of CV-QKD, particularly in constrained devices with limited storage and computational resources.
Continuous-variable (CV) quantum key distribution (QKD) employs the quadratures of a bosonic mode to establish a secret key between two remote parties, and this is usually achieved via a Gaussian modulation of coherent states. The resulting secret key rate depends not only on the loss and noise in the communication channel, but also on a series of data processing steps that are needed for transforming shared correlations into a final string of secret bits. Here we consider a Gaussian-modulated coherent-state protocol with homodyne detection in the general setting of composable finite-size security. After simulating the process of quantum communication, the output classical data are postprocessed via procedures of parameter estimation, error correction, and privacy amplification. In particular, we analyze the high signal-to-noise regime, which requires the use of high-rate (nonbinary) low-density parity check codes. We implement all these steps in a python-based library that allows one to investigate and optimize the protocol parameters to be used in practical experimental implementations of short-range CV-QKD.
Quantum key distribution (QKD) guarantees information-theoretic security by the laws of physics, but deployment at scale requires compact, manufacturable photonic terminals. Continuous-variable QKD (CV-QKD) is well suited for this transition through telecom-compatible, room-temperature coherent detection. However, unifying full on-chip core terminal integration, room-temperature operation, high loss tolerance, and composable end-to-end security in long-distance QKD remains a key bottleneck. Here we report a fully integrated CV-QKD platform in which two hybrid III--V/Si3_33​N4_44​ integrated lasers, a silicon transmitter, and a silicon coherent receiver implement the core terminal functions, operating with a local local oscillator (LLO) over fibre links of 25--150 km. A Bayesian machine-learning algorithm maintains robust phase lock throughout the long records required for composable security, consistently outperforming the conventional unscented Kalman filter, while rate-matched multidimensional reconciliation approaches the Shannon limit. The system certifies a composable finite-size secret-key rate of 29.3 kbps at 100 km from a 140-billion-symbol block, with 12.9 kbps at 125 km under finite-size analysis and 9.17 kbps at 150 km under asymptotic analysis. By establishing the longest finite-size and asymptotic reaches and the highest secret-key rate per symbol reported for integrated CV-QKD, this work advances the development of practical chip-based quantum networks.
This technical report proposes a unified error correction and reconciliation framework designed specifically for improving the secure key rate of Quantum Key Distribution (QKD) protocols, particularly in Continuous-Variable (CV-QKD) systems. Problem Addressed: Existing QKD reconciliation methods rely on standard binary codes, which fail to leverage the inherent geometry of the lattice channels used in CV-QKD. This leads to reduced efficiency, especially when the signal quality is low (low SNR). Key Innovations: Lattice-Native Coding: The design employs Low-Density Parity-Check (LDPC) codes defined natively over integer rings (Z-sub-q), allowing direct alignment with the geometric structure of the quantum channel. Geometry-Preserving Interleaving: A novel, low-discrepancy interleaver is introduced to optimize error spreading while maintaining local geometric structure during encoding and decoding. Leak-Aware Reconciliation Ledger: A dynamic ledger is used to precisely track all information leakage (syndrome sum) during the error correction process. This tracked leakage directly sets the length for Privacy Amplification, ensuring rigorous and composable finite-key security bounds.
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.
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 quantum key distribution (CV-QKD) enables two remote parties to establish information-theoretically secure keys and offers high practical feasibility due to its compatibility with mature coherent optical communication technologies. However, as CV-QKD systems progress toward digital implementations, device nonidealities drive the optical field from a single-mode to a continuous-mode region, thereby underscoring the mismatch between theoretical models and practical systems. Here, we introduce temporal modes to construct an entanglement-based scheme that more accurately captures device nonidealities and develop a corresponding secret key rate calculation method applicable to continuous-mode scenarios. We demonstrate that optimizing the pulse-shaping format can significantly improve performance under detector-bandwidth-limited conditions. Experimental results also confirm that the proposed model effectively describes the impact of sampling-time deviations. We further analyze a linear weighted-reconstruction digital signal processing method,which improves the secret key rate by approximately 50% in a 30-km fiber experiment without requiring additional hardware, demonstrating a substantial performance enhancement at metropolitan distances. The proposed theoretical framework accommodates a broader range of experimental conditions and can guide the optimization of digital CV-QKD systems.