Continuous-mode analysis for practical continuous-variable quantum key distribution

Continuous-variable quantum key distribution (CV-QKD) enables two remote parties to establish information-theoretically secure keys and offers high practical feasibility due to its compatibility with mature coherent optical communication technologies. However, as CV-QKD systems progress toward digital implementations, device nonidealities drive the optical field from a single-mode to a continuous-mode region, thereby underscoring the mismatch between theoretical models and practical systems. Here, we introduce temporal modes to construct an entanglement-based scheme that more accurately captures device nonidealities and develop a corresponding secret key rate calculation method applicable to continuous-mode scenarios. We demonstrate that optimizing the pulse-shaping format can significantly improve performance under detector-bandwidth-limited conditions. Experimental results also confirm that the proposed model effectively describes the impact of sampling-time deviations. We further analyze a linear weighted-reconstruction digital signal processing method,which improves the secret key rate by approximately 50% in a 30-km fiber experiment without requiring additional hardware, demonstrating a substantial performance enhancement at metropolitan distances. The proposed theoretical framework accommodates a broader range of experimental conditions and can guide the optimization of digital CV-QKD systems.