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Journal of Physics A Mathematical and Theoretical

Security boundaries of two-way continuous-variable quantum key distribution under multiple source imperfections

Ningyi Mao, Hang Zhang, Zhiyue Zuo, Yiyu Mao, Yue Wang, Ying Guo

Published May 26, 2026• 0 citations
Publisher

Abstract

Abstract Two-way continuous-variable quantum key distribution protocol, where the parties make a double use of the quantum channel, shows the general superadditivity in the security thresholds, which are proven to be higher than that of the classical one-way protocol. However, all existing security proofs for two-way protocols assume perfect source devices or a trusted source noise, which is hard to ensure in a practical system. In this paper, the effects of multiple source fluctuations on the security of the two-way protocol are proposed, where Eve may have access to the intensity fluctuation information with an arbitrary random distribution. This work is comprehensive of several practical scenarios, encompassing both ON and OFF configurations, with and without the assumption that trusted users can access the fluctuation information. The analysis shows that when the users have no fluctuation information, the intensity fluctuation effect in the ON configuration should be modeled as an additional thermal noise rather than being described by a beam splitter model as in the general one-way protocol. In addition, this untrusted noise is only related to the intensity fluctuation variance but has no relation to its distribution. Finally, the tagging idea is applied to the two-way protocol to obtain a conservative secure key.

DOI
10.1088/1751-8121/ae72d4

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Abstract Two-way continuous-variable quantum key distribution protocol, where the parties make a double use of the quantum channel, shows the general superadditivity in the security thresholds, which are proven to be higher than that of the classical one-way protocol. However, all existing security proofs for two-way protocols assume perfect source devices or a trusted source noise, which is hard to ensure in a practical system. In this paper, the effects of multiple source fluctuations on the security of the two-way protocol are proposed, where Eve may have access to the intensity fluctuation information with an arbitrary random distribution. This work is comprehensive of several practical scenarios, encompassing both ON and OFF configurations, with and without the assumption that trusted users can access the fluctuation information. The analysis shows that when the users have no fluctuation information, the intensity fluctuation effect in the ON configuration should be modeled as an additional thermal noise rather than being described by a beam splitter model as in the general one-way protocol. In addition, this untrusted noise is only related to the intensity fluctuation variance but has no relation to its distribution. Finally, the tagging idea is applied to the two-way protocol to obtain a conservative secure key.
We investigate the security of reverse reconciliation two-way continuous-variable quantum key distribution with source noise at both legitimate sides. Because the source noise originates from imperfect devices, we ascribe it to the legitimate sides rather than the eavesdropper. The trusted model consists of a thermal noise injected into a beam splitter. The expressions of secret key rate are derived against collective entangling cloner attacks for homodyne and heterodyne detections. Simulation results show that by applying the trusted model, the security bound of the reverse reconciliation two-way protocols can be tightened, while the advantage over one-way protocols still maintains.
Abstract Despite tremendous theoretical and experimental progress in continuous variable (CV) quantum key distribution (QKD), the security has not been rigorously established for most current continuous variable quantum key distribution systems that have imperfections. Among these imperfections, intensity fluctuation is one of the principal problems affecting security. In this paper, we provide simple security proofs for continuous variable quantum key distribution systems with intensity fluctuating sources. Specifically, depending on device assumptions in the source, the imperfect systems are divided into two general cases for security proofs. In the most conservative case, we prove the security based on the tagging idea, which is a main technique for the security proof of discrete variable quantum key distribution. Our proofs are simple to implement without any hardware adjustment for current continuous variable quantum key distribution systems. Also, we show that our proofs are able to provide secure secret keys in the finite-size scenario.
Despite tremendous theoretical and experimental progress in continuous variable (CV) quantum key distribution (QKD), its security has not been rigorously established for practical systems with multiple imperfections. The idea of tagging is widely used in security proofs of discrete variable quantum key distribution with imperfect devices. In this paper, we generalize the tagging idea from discrete variable to continuous variable. Based on untagged signals, we prove the security of the imperfect quantum key distribution system in the most conservative case. By introducing a generic imperfection model, we can evaluate and further incorporate multiple imperfections in the different stages such as modulation, channel and detection. Finally, with this generic model and tagging idea, we can prove the security of continuous variable key distribution system with multiple imperfections. Our case study shows our proofs are able to provide secure keys in the presence of both modulation and detection flaws.
Subject of study. Two-way continuous-variable quantum key distribution schemes are studied. Aim. This study aims to prove the security of the plug-and-play continuous-variable quantum key distribution system in the context of the model of trusted noise from legitimate users. Method. Based on an analog of the well-known implementation in the plug-and-play format, the performance of such a system operating under the GG02 protocol is evaluated. The evaluation is conducted in the presence of collective attacks, considering the finite-key effects. Main results. A secure key that satisfies the composability criteria can be distributed with a channel loss of 5 dB, which is expected to be approximately half that in a one-way scheme. Practical significance. Two-way quantum key distribution schemes are more stable than one-way schemes, and hence, their stability requires detailed consideration. This paper is the first, to our knowledge, to propose considering the security of a two-way implementation of continuous-variable quantum key distribution, considering the trusted equipment noise.
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.
We consider two-way continuous-variable quantum key distribution, studying its security against general eavesdropping strategies. Assuming the asymptotic limit of many signals exchanged, we prove that two-way Gaussian protocols are immune to coherent attacks. More precisely we show the general superadditivity of the two-way security thresholds, which are proven to be higher than the corresponding one-way counterparts in all cases. We perform the security analysis first reducing the general eavesdropping to a two-mode coherent Gaussian attack, and then showing that the superadditivity is achieved by exploiting the random on/off switching of the two-way quantum communication. This allows the parties to choose the appropriate communication instances to prepare the key, accordingly to the tomography of the quantum channel. The random opening and closing of the circuit represents, in fact, an additional degree of freedom allowing the parties to convert, a posteriori, the two-mode correlations of the eavesdropping into noise. The eavesdropper is assumed to have no access to the on/off switching and, indeed, cannot adapt her attack. We explicitly prove that this mechanism enhances the security performance, no matter if the eavesdropper performs collective or coherent attacks.