Route Planning and Online Routing for Quantum Key Distribution Networks
Jorge López, Charalampos Chatzinakis, Marc Cartigny
TL;DR
The paper tackles the challenge of route planning and online routing in Quantum Key Distribution (QKD) networks, where capacity-constrained quantum links make traditional shortest-path routing ineffective. It models QKD networks as directed graphs with edge capacities and introduces two problems: Route Planning with Fair Automated Suggestions for Unfeasible Instances (RPFASUI) and Single Online Routing Request (SORR); RPFASUI is tackled via a Quadratic Programming formulation to fairly allocate bandwidth, while SORR analyzes online routing strategies under worst-case demand. The authors derive competitive-ratio guarantees for online routing: the shortest available path achieves a worst-case ratio of $\frac{1}{1+\mu\left\lfloor\frac{|E|}{2}\right\rfloor}$, while the widest-shortest path attains at least $\frac{1}{2}$ (and a refined bound $\frac{1}{2}+\frac{1}{2+4\mu(|E|-1)}$ under certain conditions). Empirical evaluation across diverse topologies confirms the theoretical findings, showing that widest-path strategies offer more robust performance than shortest-path in both worst-case and realistic random settings; the work also outlines future directions such as multi-path routing, average-case analysis, and deployment with real data.
Abstract
Quantum Key Distribution (QKD) networks harness the principles of quantum physics in order to securely transmit cryptographic key material, providing physical guarantees. These networks require traditional management and operational components, such as routing information through the network elements. However, due to the limitations on capacity and the particularities of information handling in these networks, traditional shortest paths algorithms for routing perform poorly on both route planning and online routing, which is counterintuitive. Moreover, due to the scarce resources in such networks, often the expressed demand cannot be met by any assignment of routes. To address both the route planning problem and the need for fair automated suggestions in infeasible cases, we propose to model this problem as a Quadratic Programming (QP) problem. For the online routing problem, we showcase that the shortest (available) paths routing strategy performs poorly in the online setting. Furthermore, we prove that the widest shortest path routing strategy has a competitive ratio greater or equal than $\frac{1}{2}$, efficiently addressing both routing modes in QKD networks.