Coding for High-Dimensional Quantum Key Distribution. A PhD thesis

The relentless progress of increasingly powerful (quantum) computers and more efficient algorithms poses a continuous challenge to modern cryptography. Quantum Key Distribution (QKD) has the potential to meet this challenge by guaranteeing information-theoretic secure communication. QKD is an active research area and a mature technology with industrial demand and commercial availability. A significant contribution to the performance of any QKD system is the Information Reconciliation phase (IR), which removes mismatches between distributed keys. Optimizing this phase can further increase the communication rate of QKD systems. Another approach to enhancing the communication rate is deploying high-dimensional quantum states instead of binary systems, in high-dimensional QKD systems (HD-QKD). Over three years of research, this thesis explored and optimized the IR phase, HD-QKD systems, and their combination, IR for HD-QKD. Specifically, we have demonstrated and analyzed different IR solutions for practical and industrial settings on binary QKD systems. This analysis includes their performance with respect to efficiency, throughput, and exchanged messages under varying QBER, mismatching QBER estimates, and realistic channel noise. Further, we explored the possibility of generalizing a specific high-performing QKD system to higher dimensions: (high-dimensional) Twin-Field QKD. The core contribution of this thesis lies in the topic of IR for HDQKD systems, where we present and analyze three novel and effective approaches in this largely unexplored field: NONBINARY, nonbinary LDPC codes, and Highdimensional Cascade. We describe these approaches in detail and show that they achieve good efficiencies even for high dimensional channels, and discuss the different scenarios in which each approach can see application.