Digital Signal Processing from Classical Coherent Systems to Continuous-Variable QKD: A Review of Cross-Domain Techniques, Applications, and Challenges

This systematic review investigates the application of digital signal processing (DSP) techniques -- originally developed for coherent optical communication systems to continuous-variable quantum key distribution (CV-QKD). The convergence of these domains has enabled significant advances in CV-QKD performance, particularly in phase synchronization, polarization tracking, and excess noise mitigation. To provide a comprehensive and reproducible synthesis of this emerging field, we employed the APISSER methodology, a task-oriented framework adapted from the PRISMA protocol. A structured search across IEEE Xplore and Web of Science databases (2021-2025) yielded 220 relevant publications, which were screened, classified, and analyzed to address six research questions. Our findings highlight that many classical DSP algorithms, such as Kalman filtering, carrier recovery, adaptive equalization, and machine-learning-assisted signal estimation, have been successfully adapted to the quantum regime, often requiring modifications to meet security and noise constraints. We also identify a range of recent DSP innovations in coherent optical communication systems with high potential for future CV-QKD integration, including neural equalization, probabilistic shaping, and joint retiming-equalization filters. Despite these advances, challenges remain in achieving robust phase tracking under ultra-low Signal-to-Noise Ratio (SNR) conditions, real-time polarization compensation, and secure co-existence with classical channels. This review maps current trends, technical barriers, and emerging opportunities at the intersection of signal processing for quantum and classical communication, supporting the development of scalable and resilient CV-QKD systems.