Quantum catalysis has been proven to be effective in improving the performance of Gaussian modulation continuous variable quantum key distribution (CVQKD) protocols, significantly enhancing secure transmission distances. However, there is currently a lack of research on utilizing quantum catalysis to improve the performance of four-state modulation protocols. This paper focuses on enhancing the one-dimensional four-state modulation continuous variable quantum key distribution protocol using quantum catalysis. While Gaussian modulation CVQKD protocols offer the advantage of higher secure key rates, their secure transmission distances are limited. On the other hand, discrete modulation protocols exhibit better performance in terms of transmission distances. Additionally, to further simplify the protocol complexity, we adopt a one-dimensional modulation approach. This not only reduces the implementation cost and complexity but also enhances the robustness, secure key rates, and transmission distances of the protocol.
Quantum catalysis has been proven to be effective in improving the performance of Gaussian modulation continuous variable quantum key distribution (CVQKD) protocols, significantly enhancing secure transmission distances. However, there is currently a lack of research on utilizing quantum catalysis to improve the performance of four-state modulation protocols. This paper focuses on enhancing the one-dimensional four-state modulation continuous variable quantum key distribution protocol using quantum catalysis. While Gaussian modulation CVQKD protocols offer the advantage of higher secure key rates, their secure transmission distances are limited. On the other hand, discrete modulation protocols exhibit better performance in terms of transmission distances. Additionally, to further simplify the protocol complexity, we adopt a one-dimensional modulation approach. This not only reduces the implementation cost and complexity but also enhances the robustness, secure key rates, and transmission distances of the protocol.
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.
Abstract Discrete modulation can make up for the shortage of transmission distance in measurement-device-independent continuous-variable quantum key distribution (MDI-CVQKD), providing a unique advantage against all side-channel attacks but also creating a challenge for further performance improvement. Here we suggest a quantum catalysis (QC) approach for enhancing the performance of the discrete-modulated (DM) MDI-CVQKD in terms of the achievable secret key rate and lengthening the maximal transmission distance. The numerical simulation results show that the QC-based MDI-CVQKD with discrete modulation, involving a zero-photon catalysis (ZPC) operation, can not only obtain a higher secret key rate than the original DM protocol, but also contribute to a reasonable increase of the corresponding optimal variance. As for the extreme asymmetric and symmetric cases, the secret key rate and maximal transmission distance of the ZPC-involved DM MDI-CVQKD system can be further improved under the same parameters. This approach enables the system to tolerate lower reconciliation efficiency, which may provide excellent potential for practical implementations with state-of-art technology.
The non-Gaussian operation can be used not only to enhance and distill the entanglement between Gaussian entangled states, but also to improve the performance of quantum communications. In this paper, we propose a non-Gaussian continuous-variable quantum key distribution (CVQKD) by using quantum catalysis (QC), which is an intriguing non-Gaussian operation in essence that can be implemented with current technologies. We perform quantum catalysis on both ends of the Einstein-Podolsky-Rosen pair prepared by a sender, Alice, and find that for the single-photon QC-CVQKD, the bilateral symmetrical quantum catalysis performs better than the single-side quantum catalysis. Attributing to characteristics of an integral within an ordered product of operators, we find that the quantum-catalysis operation can improve the entanglement property of Gaussian entangled states by enhancing the success probability of non-Gaussian operation, leading to the improvement of the QC-CVQKD system. As a comparison, the QC-CVQKD system involving zero-photon and single-photon quantum catalysis outperforms the previous non-Gaussian CVQKD scheme via photon subtraction in terms of a secret key rate, maximal transmission distance, and tolerable excess noise.
Continuous-variable quantum key distribution (CV-QKD) provides an effective way to obtain the high secret key rate, but is limited by practical techniques. To overcome this limitation, we investigate the performance of CV-QKD protocols when non-Gaussian operations are applied to both sides of the channels, including photon subtraction and addition, and photon catalysis. A comparison is also made between Gaussian modulation and non-Gaussian modulation. We show that the optimal transmission distance cannot be improved by non-Gaussian modulation at the sender's side, but it can be improved by single-photon catalysis at the receiver's side. For a given modulation variance that exceeds a certain threshold, the performance of the zero-photon catalysis at the sender's side is the best when compared with other non-Gaussian modulations (except single-photon catalysis at the receiver's side), and it can always reach the optimal distance. Our paper will provide a useful insight for the use of non-Gaussian modulation to other CV-QKD protocols.
Quantum catalysis is a feasible approach to increase the performance of continuous-variable quantum key distribution (CVQKD), involving the special zero-photon catalysis (ZPC) operation. However, in the practical point of view, the improvement effect of this operation will be limited by the imperfection of the photon detector. In this paper, we show that the ZPC operation at the sender can be simulated by a post-selection method without implementing it in practical devices. While performing this virtual version of ZPC in CVQKD, we can not only reach the ideal case of its practical implementation with minimal hardware requirement, but also keep the benefit of Gaussian security proofs. Based on Gaussian modulated coherent state protocols with achievable parameters, we enhance the security of the proposed scheme from the asymptotical case to the finite-size scenario and composable framework. Simulation results show that similar to the asymptotical case, both the maximal transmission distance and the tolerable excess noise of virtual ZPC-involved CVQKD outperform the original scheme and the scheme using virtual photon subtraction while considering finite-size effect and composable security. In addition, the virtual ZPC-involved CVQKD can tolerate a higher imperfection of the detector, enabling its practical implementation of the CVQKD system with state-of-the-art technology.
The modulation mode at the transmitters plays a crucial role in the continuous-variable measurement-device-independent quantum key distribution (CV-MDI-QKD) protocol. However, in practical applications, differences in the modulation schemes between two transmitters can inevitably impact protocol performance, particularly when using discrete modulation with four-state or eight-state formats. This work primarily investigates the effect of imbalanced modulation at the transmitters on the security of the CV-MDI-QKD protocol under both symmetric and asymmetric distance scenarios. By employing imbalanced discrete modulation maps and numerical convex optimization techniques, the proposed CV-MDI-QKD protocol achieves a notably higher secret key rate and outperforms existing protocols in terms of maximum transmission distance. Specifically, simulation results demonstrate that the secret key rate and maximum transmission distance are boosted by approximately 77.77% and 24.3%, respectively, compared to the original protocol. This novel and simplified modulation method can be seamlessly implemented in existing experimental setups without requiring equipment modifications. Furthermore, it provides a practical approach to enhancing protocol performance and enabling cost-effective applications in secure quantum communication networks under real-world environments.