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.
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.
Abstract In this paper, the performance of a unidimensional continuous variable quantum key distribution protocol is analyzed using Gaussian modulated coherent state under fast fading channel. In the fast fading channel, both parties are connected in free space, resulting in a harsh propagation environment and pollution caused by atmospheric turbulence. This pollution makes it difficult for the communicators to determine the channel transmittance, which can only be estimated based on a probability distribution. To address this, only one modulator is used to code, which demonstrates performance equivalent to that of the symmetric modulated Gaussian coherent state protocol. The security of the protocol in the face of collective attacks is analyzed and it is proved that it can accept a certain amount of excessive channel noise while simplifying operations. Simultaneously, the impact of finite‐key length effects on the protocol is analyzed. It is also demonstrated that this protocol can reduce costs within an acceptable range of performance losses, making it more practical.
Compared with discrete variable quantum key distribution (DVQKD), continuous variable (CV) QKD has high security bit rate and other advantages, which, however, are slightly insufficient in secure transmission distance. In addition, the application of quantum catalysis has significantly improved the performance of Gaussian modulated (GM) CVQKD, especially in secure transmission distance. Recently, the application of quantum catalysis has significantly improved the performance of GM-CVQKD. However, whether it can be used to improve the performance of discrete modulated (DM) CVQKD protocol is still ambiguous. Therefore, a scheme of DM CVQKD protocol based on quantum catalysis is proposed in this paper to further improve the performance of the proposed protocol in terms of secure key rate, secure transmission distance and maximum tolerable noise. Our results show that under the same parameters, when the transmittance T introduced by quantum catalysis is optimized, the proposed scheme can effectively further improve the performance of QKD system compared with the original four-state modulation CVQKD scheme. In particular, when the tolerable excess noise is 0.002, the use of quantum catalysis can break the safe communication distance of 300 km with a key rate of 10–8 bits/pulse. However, if this noise is too large, the improvement in the effect of quantum catalysis on protocol performance will be restrained. In addition, in order to highlight the advantages of the use of quantum catalysis, the ultimate limit PLOB (Pirandola-Laurenza-Ottaviani-Banchi) bound of point-to-point quantum communication is given in this paper. The simulation results indicate that although neither the original scheme nor the proposed scheme can break the bound, compared with the former, the latter can be close to the boundary in long-distance transmission. These results provide theoretical basis for achieving the ultimate goal of global quantum security communication.
The discretely modulated continuous-variable quantum key distribution (DM CVQKD) has been proven to be secure, and a basic assumption for the current theoretical security proof of the DM CVQKD is that the signal source cannot be compromised. However, this assumption is quite unpractical in real quantum communication systems. In this paper, we investigate the DM CVQKD with a special configuration in which the entanglement source is placed at the untrusted channel. With this configuration, the source is no longer protected by the sender but is exposed to the vulnerable environment. In particular, we consider the configuration for two typical DM CVQKD protocols, which are the four-state protocol and the eight-state protocol. Security analysis based on linear bosonic channel shows that the DM CVQKD with an untrusted entanglement source is able to defend itself against the most powerful quantum collective attack in a certain distance range and it can still generate positive secret key rate when considering finite-size effect and composable security, thereby providing a theoretical proof for applying the DM CVQKD system to a realistic environment.
Continuous variable quantum key distribution (CV-QKD) has emerged as a promising candidate for quantum-secure communication due to its experimentally demonstrated high key rates in fiber-optic channels. However, the feasibility of discrete modulation CV-QKD in satellite-to-ground downlinks remains an open question due to practical challenges such as high transmission loss, limited communication windows, and atmospheric turbulence. In this work, a comprehensive framework is proposed to evaluate the feasibility of discrete modulation CV-QKD by integrating orbital dynamics and atmospheric channel models, and to comprehensively analyze the influence of the parameter space on free-space discrete modulation CV-QKD. To achieve this, a free-space CV-QKD simulation platform is employed, which calculates the elevation angle and transmission distance based on precise orbital models, thereby providing a more practical assessment of the key rate for discrete modulation CV-QKD. Simulation results verify the feasibility and practicality of discrete modulation CV-QKD in satellite-based quantum communication systems. Furthermore, the critical factors influencing the key rate performance are identified, and parameter optimization strategies are proposed, providing theoretical support for realizing the future satellite-to-ground discrete modulation CV-QKD.
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.
Quantum key distribution (QKD) offers a promising solution by providing information-theoretic security based on the principles of quantum mechanics. Beyond theoretical experiments, QKD network construction and verification are actively progressing in various locations worldwide. Continuousvariable QKD (CVQKD) has emerged as a strong candidate for integration into optical networks, particularly due to its compatibility with coherent detection schemes used in existing optical communication systems. Gaussian-modulated (GM) CVQKD enables simpler security analysis through covariance matrices, but its practical implementation typically requires highperformance optical components, leading to increased cost and complexity. In contrast, discrete-modulated (DM) CVQKD using modulation formats, such as quadrature amplitude modulation (QAM), can reduce implementation costs by utilizing the existing optical components. However, its security analysis requires more advanced techniques due to the non-Gaussian nature of the quantum states involved. This study evaluates the performance of GM- and DM-CVQKD under a common optical fiber channel model. Our results show that the secure key rates (SKRs) of DM-CVQKD with probabilistic constellation shaping (PCS) 64QAM and PCS-256QAM drop below zero at transmission distances of 277 km and 399 km, respectively. The results confirm the feasibility of DM-CVQKD for long-distance secure communication over optical fiber networks when appropriate modulation formats and PCS are employed.