Improving One-Dimensional Four-State Modulation Continuous Variable Quantum Key Distribution with Quantum Catalysis

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.