Secure quantum key distribution against correlated leakage source.

Quantum key distribution (QKD) provides information-theoretic security based on quantum mechanics, yet its implementation is hindered by source imperfections. Among these, correlations between transmitted pulses present a critical but underexplored threat to QKD's theoretical security. We propose a general framework for QKD security under correlated sources, achieving the first finite-key analysis by extending and reorganizing QKD rounds using the generalized chain rule. Inspired by side-channel-secure QKD, we design a protocol secure against correlated leakage sources, requiring only the correlation range and lower bounds on the vacuum component of the prepared states. Our framework also applies to other QKD protocols, providing a general approach to address correlation-induced vulnerabilities. Simulations demonstrate the effectiveness of our protocol and its significantly superior tolerance to imperfections compared to existing protocols. This work provides a crucial step toward closing security loopholes in QKD, enhancing its practicality, and ensuring long-distance, high-performance secure communication under real-world constraints.