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.

翻译：量子密钥分发（QKD）网络利用量子物理原理安全传输密码密钥材料，提供物理层面的安全保障。这类网络需要传统管理和操作组件，例如通过网络单元进行路由信息传递。然而，由于容量限制及此类网络中信息处理的特殊性，传统的最短路径路由算法在路径规划和在线路由方面均表现不佳，这一现象有违直觉。此外，由于此类网络资源稀缺，通常无法通过任何路由分配满足所表达的需求。为解决路径规划问题及在不可行情况下提供公平自动化建议的需求，我们提出将该问题建模为二次规划（QP）问题。针对在线路由问题，我们证明最短（可用）路径路由策略在在线场景中表现较差。进一步地，我们证明最宽最短路径路由策略的竞争比大于或等于 $\frac{1}{2}$，从而有效解决了QKD网络中的两种路由模式。