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Physica Scripta

Two-way continuous-variable quantum key distribution in fast-fading channels

Yayou Zou, J Zhou, Weimin Yang, Guangqiang He

Published Oct 5, 2026• 0 citations
Publisher

Abstract

Abstract This paper presents a theoretical benchmark analysis of selected two-way continuous-variable quantum key distribution protocols over fast-fading channels. For uniformly fluctuating transmissivity, a non-CSI benchmark treatment evaluates the mutual information term at the worst transmissivity and averages Eve’s information over the fading distribution. Closed-form asymptotic key-rate formulas are derived for specific two-way protocols in the large-modulation regime. The framework also applies to CSI-enabled averaging and truncated log-normal weak-turbulence fading. Numerical results show that, within the adopted ideal asymptotic setting, the evaluated two-way RoR 2 benchmark retains a broader positive-key-rate region than the corresponding one-way RoR benchmark under uniform non-CSI fading. CSI-enabled averaging and the weak-turbulence extension further characterize the behavior of the selected two-way benchmarks under different channel-knowledge and fading conditions. Overall, these results characterize the performance of the selected two-way protocols across the adopted fast-fading benchmark settings.

DOI
10.1088/1402-4896/aeb051

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Abstract This paper presents a theoretical benchmark analysis of selected two-way continuous-variable quantum key distribution protocols over fast-fading channels. For uniformly fluctuating transmissivity, a non-CSI benchmark treatment evaluates the mutual information term at the worst transmissivity and averages Eve’s information over the fading distribution. Closed-form asymptotic key-rate formulas are derived for specific two-way protocols in the large-modulation regime. The framework also applies to CSI-enabled averaging and truncated log-normal weak-turbulence fading. Numerical results show that, within the adopted ideal asymptotic setting, the evaluated two-way RoR 2 benchmark retains a broader positive-key-rate region than the corresponding one-way RoR benchmark under uniform non-CSI fading. CSI-enabled averaging and the weak-turbulence extension further characterize the behavior of the selected two-way benchmarks under different channel-knowledge and fading conditions. Overall, these results characterize the performance of the selected two-way protocols across the adopted fast-fading benchmark settings.
We investigate the performance of several continuous-variable quantum key distribution protocols in the presence of uniform fading channels. These are lossy channels whose transmissivity changes according to a uniform probability distribution. We assume the worst-case scenario where an eavesdropper induces a fast-fading process, where she chooses the instantaneous transmissivity while the remote parties may only detect the mean statistical effect. We analyze coherent-state protocols in various configurations, including the one-way switching protocol in reverse reconciliation, the measurement-device-independent protocol in the symmetric configuration, and its extension to a three-party network. We show that, regardless of the advantage given to the eavesdropper (control of the fading), these protocols can still achieve high rates under realistic attacks, within reasonable values for the variance of the probability distribution associated with the fading process.
In this thesis we study the finite-size analysis of two continuous-variables quantum key distribution schemes. The first one is the one-way protocol using Gaussian modulation of thermal states and the other is the measurement-device-independent protocol. To do so, we adopt an efficient channel parameter estimation method based on the assumption of the Gaussian variables and the central limit theorem introduced by Ruppert et al. [Phys. Rev. A 90, 062310 (2014)]. Furthermore, we present a composable security analysis of the measurement device independent protocol for coherent attacks with a channel parameter estimation that is not based on the central limit theorem. We also investigated, in the asymptotic regime, an asymmetric situation for the authenticated parties against the eavesdropper caused by fast-fading channels. Here we assume that the eavesdropper has the full control of the communication channel and can instantaneously change its transmissivity in every use of it. We assumed the simple model of a uniform fading and addressed the cases of one-way protocols, continuous-measurement device-independent protocol in symmetric configuration and its star network extension for three users. Finally, we extended the asymptotic study of the one-way protocols using an arbitrary number of phase-encoded coherent states assuming a thermal loss channel without using a Gaussian approximation.
Abstract After decades of development, continuous variable quantum key distribution technology still cannot meet people’s needs for secure communication over long distances. Free-space quantum communication provides a new way for secure communication over long distances. However, because the communication connected in free space is inevitably affected by atmospheric turbulence, the transmission rate of the channel changes rapidly according to the probability distribution, making it difficult for the communication personnel to determine the transmission rate of the channel. At the same time, discrete modulated continuously variable quantum key Distribution protocol (DM-CVQKD) has certain advantages over Gauss modulated continuously variable quantum key Distribution protocol (GM-CVQKD) in the communication distance. Therefore, this paper analyzes the key rate of DM-CVQKD in this case (that is, in the fast attenuation channel), proves that it can resist the collective attack, and observes the relationship between the parameters and the key rate in the fast attenuation channel by numerical simulation and control variables. Finally, through the analysis of numerical simulation results, it is found that DM-CVQKD can still maintain a high key rate under certain conditions, which proves that long-distance free space quantum communication is feasible under certain conditions. At the same time, it was found that the performance of DM-CVQKD was affected by the extreme case where Eve completely controlled the instantaneous transmittance.
This work presents a study of continuous-variable quantum key distribution (CV-QKD) protocols over fast-fading channels, typically found in free-space communication links. Two eavesdropping models are considered to evaluate their security under collective attacks: \textit{Holevo bound average} (HBA) and \textit{covariance matrix average} (CMA). In the HBA approach, the Holevo bound is averaged over the channel transmittance. In contrast, the CMA method calculates the Holevo bound from the average covariance matrix. Analytical expressions are developed for both strategies. The two methods also differ in how they calculate the mutual information between the legitimate parties. The results demonstrate that the SKR is significantly influenced by how you treat channel fluctuations, highlighting the importance of choosing the model that better describes the actual implementation of the protocol.
Abstract This study examines the implementation of continuous-variable quantum key distribution (CV-QKD) using thermal states via fast fading channel. In such channel, communication occurs in free space under adverse conditions such as atmospheric turbulence, causing the channel transmittance to vary according to a specific mathematical probability. In worst-case scenarios, an eavesdropper could fully control the channel, leaving communicators to make pessimistic assumptions about channel conditions. The security of this system is analyzed and evaluated using homodyne and heterodyne detection methods under reverse reconciliation. The results indicate that even with full eavesdropper control, employing noise sources in CV-QKD ensures high key rates and protocol security. Furthermore, it has been demonstrated that the introduction of preparation noise in heterodyne detection is more effective than homodyne detection under fast fading channel conditions.
Continuous variable quantum key distribution enables two parties to extract provably secure keys for cryptography by exploiting aspects of quantum mechanics. A central challenge in achieving QKD over long distances is overcoming optical loss, which limits the secret key rates and achievable transmission distances. Recent work has illustrated how to perform continuous variable quantum key distribution while eliminating information leakage to an eavesdropper in a pure-loss channel and minimizing information leakage in a noisy channel. In this work, we analyse this protocol under conditions where the quantum channel linking the sender and receiver is a fading channel, which can be used to model free-space links. We find that the protocol maintains strong performance over fading channels and outperforms comparable protocols.