Rigorous phase-error-estimation security framework for QKD with correlated sources

Practical QKD modulators introduce correlations between consecutively emitted pulses due to bandwidth limitations, violating key assumptions underlying many security proof techniques. Here, we address this problem by introducing a simple yet powerful mathematical framework to directly extend phase-error-estimation-based security proofs for imperfect but uncorrelated sources to also incorporate encoding correlations. Our framework overcomes important limitations of previous approaches in terms of generality and rigor, significantly narrowing the gap between theoretical security guarantees and real-world QKD implementations.