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arXiv:1206.6357 · Physical Review A

Analysis of imperfections in practical continuous-variable quantum key distribution

Paul Jouguet, Sébastien Kunz-Jacques, Eleni Diamanti, Anthony Leverrier

Published Sep 10, 2012• 233 citations
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Abstract

As quantum key distribution becomes a mature technology, it appears clearly that some assumptions made in the security proofs cannot be justified in practical implementations. This might open the door to possible side-channel attacks. We examine several discrepancies between theoretical models and experimental setups in the case of continuous-variable quantum key distribution. We study in particular the impact of an imperfect modulation on the security of Gaussian protocols and show that approximating the theoretical Gaussian modulation with a discrete one is sufficient in practice. We also address the issue of properly calibrating the detection setup and in particular the value of the shot noise. Finally, we consider the influence of phase noise in the preparation stage of the protocol and argue that taking this noise into account can improve the secret key rate because this source of noise is not controlled by the eavesdropper.

DOI
10.1103/physreva.86.032309

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As quantum key distribution becomes a mature technology, it appears clearly that some assumptions made in the security proofs cannot be justified in practical implementations. This might open the door to possible side-channel attacks. We examine several discrepancies between theoretical models and experimental setups in the case of continuous-variable quantum key distribution. We study in particular the impact of an imperfect modulation on the security of Gaussian protocols and show that approximating the theoretical Gaussian modulation with a discrete one is sufficient in practice. We also address the issue of properly calibrating the detection setup and in particular the value of the shot noise. Finally, we consider the influence of phase noise in the preparation stage of the protocol and argue that taking this noise into account can improve the secret key rate because this source of noise is not controlled by the eavesdropper.
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We address side-channel leakage in a trusted preparation station of continuous-variable quantum key distribution with coherent and squeezed states. We consider two different scenarios: multimode Gaussian modulation, directly accessible to an eavesdropper, or side-channel loss of the signal states prior to the modulation stage. We show the negative impact of excessive modulation on both the coherent- and squeezed-state protocols. The impact is more pronounced for squeezed-state protocols and may require optimization of squeezing in the case of noisy quantum channels. Further, we demonstrate that the coherent-state protocol is immune to side-channel signal state leakage prior to modulation, while the squeezed-state protocol is vulnerable to such attacks, becoming more sensitive to the noise in the channel. In the general case of noisy quantum channels the signal squeezing can be optimized to provide best performance of the protocol in the presence of side-channel leakage prior to modulation. Our results demonstrate that leakage from the trusted source in continuous-variable quantum key distribution should not be underestimated and squeezing optimization is needed to overcome coherent state protocols.
We address the role of the phase-insensitive trusted preparation and detection noise in the security of a continuous-variable quantum key distribution, considering the Gaussian protocols on the basis of coherent and squeezed states and studying them in the conditions of Gaussian lossy and noisy channels. The influence of such a noise on the security of Gaussian quantum cryptography can be crucial, even despite the fact that a noise is trusted, due to a strongly nonlinear behavior of the quantum entropies involved in the security analysis. We recapitulate the known effect of the preparation noise in both direct and reverse-reconciliation protocols, as well as the detection noise in the reverse-reconciliation scenario. As a new result, we show the negative role of the trusted detection noise in the direct-reconciliation scheme. We also describe the role of the trusted preparation or detection noise added at the reference side of the protocols in improving the robustness of the protocols to the channel noise, confirming the positive effect for the coherent-state reverse-reconciliation protocol. Finally, we address the combined effect of trusted noise added both in the source and the detector.
The system's source noise affects the practical performance of discrete-modulated continuous-variable quantum key distribution. The good news: This noise exists inside the system and cannot be exploited by eavesdroppers, so it can be trusted. However, a lack of appropriate modeling leaves a security-key-rate gap, omitting this trusted noise. The authors propose a model for trusted source noise in the discrete-modulated protocol, successfully mitigating the negative impact of an imperfect source on system performance while maintaining security of the protocol, and thus promoting practical deployment.
Quantum Key Distribution (QKD) offers information-theoretic security grounded in the laws of quantum mechanics rather than computational assumptions. While its theoretical foundations are robust, practical implementations necessarily deviate from the idealized models assumed in security analyses, opening the door to side-channel attacks and implementation loopholes. In particular, most research to date has focused on mitigating vulnerabilities in the measurement devices, leading to the development of Measurement-Device-Independent QKD (MDI-QKD) and Twin-Field QKD (TF-QKD), which effectively close all receiver-side loopholes. By contrast, the security of the source has remained less explored, despite being critical for the overall integrity of QKD systems. The goal of this thesis is to develop security proofs that explicitly account for realistic imperfections in QKD sources. Special emphasis is placed on three main aspects: correlations between emitted pulses that violate independence assumptions, imperfect phase randomization arising from practical modulation schemes, and leakage of internal settings through passive or active side channels. By formulating rigorous methods to analyze these imperfections, the work aims to provide a framework that enables practitioners to quantify and mitigate implementation risks systematically. Additionally, this thesis seeks to clarify under which conditions the commonly used decoy-state method remains secure, and to what extent source assumptions can be relaxed without compromising performance. This thesis aims to advance the understanding of how real-world deviations impact QKD security and to contribute to the development of protocols and devices. Ultimately, this work is motivated by the ambition to help bring QKD from a theoretically promising idea to a mature technology deployable with confidence in practical scenarios.