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npj Quantum Information

Continuous-variable quantum key distribution with a leakage from digital-to-analog conversion

Xu Liu, J Sun, Tong Wang, Peng Huang, Guihua Zeng

Published Jun 25, 2026• 0 citations
Publisher

Abstract

Abstract In the field of quantum communication, investigating the practical security of systems is conducive to their deployments in real-world scenarios. In this paper, we identify and experimentally demonstrate a side-channel vulnerability within continuous-variable quantum key distribution (CV-QKD) arising from the zero-order hold (ZOH) effect in digital-to-analog conversion. As digital-to-analog converters (DACs) are indispensable for modulation in CV-QKD transmitters, this leakage constitutes an intrinsic and widespread risk. We show that the ZOH-induced spectral side lobes allow an eavesdropper to extract secret information without disturbing the main signal band. Experimental validation on a CV-QKD platform reveals a leakage of 2.68 Mbit/s against a generated secret key rate of 4.73 Mbit/s. Crucially, we propose a defense strategy that completely eliminates this vulnerability, effectively restoring the system’s implementation security. By resolving this fundamental hardware limitation, our work bridges the gap between theoretical models and practical engineering, paving the way for robust, standardized quantum communication networks.

DOI
10.1038/s41534-026-01309-9

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Abstract In the field of quantum communication, investigating the practical security of systems is conducive to their deployments in real-world scenarios. In this paper, we identify and experimentally demonstrate a side-channel vulnerability within continuous-variable quantum key distribution (CV-QKD) arising from the zero-order hold (ZOH) effect in digital-to-analog conversion. As digital-to-analog converters (DACs) are indispensable for modulation in CV-QKD transmitters, this leakage constitutes an intrinsic and widespread risk. We show that the ZOH-induced spectral side lobes allow an eavesdropper to extract secret information without disturbing the main signal band. Experimental validation on a CV-QKD platform reveals a leakage of 2.68 Mbit/s against a generated secret key rate of 4.73 Mbit/s. Crucially, we propose a defense strategy that completely eliminates this vulnerability, effectively restoring the system’s implementation security. By resolving this fundamental hardware limitation, our work bridges the gap between theoretical models and practical engineering, paving the way for robust, standardized quantum communication networks.
Abstract Distributing cryptographic keys over public channels in a way that can provide information-theoretic security is the holy grail for secure communication. This can be achieved by exploiting quantum mechanical principles in so-called quantum key distribution (QKD). Continuous-variable (CV) QKD based on coherent states, in particular, is an attractive scheme for secure communication since it requires only standard telecommunication technology that can operate at room temperature. However, a recently discovered side-channel created in the process of state preparation leads to a leakage of information about the transmitted quantum state, opening a security loophole for eavesdroppers to compromise the security of the CVQKD system. Here, we present a CVQKD system without this modulation leakage vulnerability. Our implementation is based on a baseband modulation approach and uses an in-phase and quadrature (IQ) modulator for state preparation and radio frequency heterodyne detection together with carefully designed digital signal processing for state measurement. We consider practical aspects in the implementation and demonstrate the generation of a composable secret key secure against collective attacks. This work is a step towards protecting CVQKD systems against practical imperfections of physical devices and operational limitations without performance degradation.
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.
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Encoding of key bits in the quadratures of the electromagnetic light field is an essential part of any continuousvariable quantum key distribution system. However, flaws of practical implementation can make such systems susceptible to leakage of secret information. We verify a side channel presence in an optical in-phase and quadrature modulator which is caused by limited suppression of a quantum information-carrying sideband. We investigate various strategies an unauthorized third party can exploit the vulnerability in a proof-of-concept experiment and theoretically assess the modulation leakage effect on a security of the Gaussian coherent-state continuous-variable quantum key distribution protocol and show that the leakage reduces the range of conditions which support secure key generation. Without the control of sideband modulation in practical in-phase and quadrature modulator-based systems the security can be compromised.
Quantum key distribution (QKD) has been proven to be theoretically unconditionally secure. However, any theoretical security proof relies on certain assumptions. In QKD, the assumption in the theoretical proof is that the security of the protocol is considered under the asymptotic case where Alice and Bob exchange an infinite number of signals. In the continuous-variable QKD (CV-QKD), the finite-size effect imposes higher requirements on block size and excess noise control. However, the local local oscillator (LLO) CV-QKD system cannot be considered time-invariant under long blocks, especially in cases of environmental disturbances. Thus, we propose an LLO CV-QKD scheme with time-variant parameter estimation and compensation. We first establish an LLO CV-QKD theoretical model under the temporal modes of continuous-mode states. Then, a robust method is used to compensate for arbitrary frequency shift and arbitrary phase drift in CV-QKD systems with longer blocks, which cannot be achieved under traditional time-invariant parameter estimation. Besides, the digital signal processing method predicated on high-speed reference pilots can achieve a time complexity of O (1). In the experiment, the frequency shift is up to 89.05 MHz/s and phase drift is up to 3.036 Mrad/s using a piezoelectric transducer (PZT) to simulate the turbulences in the practical channel. With a signal-to-interference ratio (SIR) of −51.67 dB , we achieve a secret key rate (SKR) of 0.29 Mbits/s with an attenuation of 16 dB or a standard fiber of 80 km. This work paves the way for future long-distance field-test experiments in the finite-size regime.
Abstract Quantum key distribution (QKD) provides secure communication using quantum mechanics, with continuous-variable QKD (CV-QKD) being an attractive solution due to its compatibility with existing telecommunication technology. Its main drawback is susceptibility to signal loss in fibres and free-space links, including satellites, which limits performance. Here we show a software-based protocol enhancing CV-QKD by applying adaptive filters at the transmitter and receiver, allowing the system to dynamically respond to changing channel conditions. Our security analysis avoids relying on Gaussian extremality, giving accurate bounds on an eavesdropper’s information. The protocol can also extract keys in regions that would normally be considered insecure. We demonstrate a threefold increase in secret-key rates compared with the best existing CV-QKD protocol, and in satellite simulations, up to a 400-fold improvement. Because it requires no hardware modifications, our method can be readily integrated into existing systems, paving the way for more practical and robust quantum communication networks.