The Proportional Fair Scheduler in Wavelength-Multiplexed Quantum Networks

Abstract: We address the problem of optimal pumping strategies in quantum networks. These networks enable secure communication by distributing entangled photon pairs to user (or node) pairs. Quantum Key Distribution (QKD) protocols, like BBM92, generate secret keys from entangled photons. While secure communication and error correction are essential for any quantum communication channel, resource contention, optimization, and fairness issues are critical for networks. In this article, we analyze the performance of quantum networks, proposing simple distributed algorithms for QKD networks generating secret keys. There are significant advantages of pumping entangled photons in QKD networks, but challenges arise in practical implementations. The underlying channels are inherently time-varying, and thus data rates fluctuate between nodes. Moreover, multiple edges (node pairs) can be pumped simultaneously, albeit at the cost of a reduced secret key rate (SKR). These temporal and spatial constraints yield a complex decision-making problem whose solutions may favor a small set of user pairs to the detriment of overall, long-run network performance. We design adaptive pumping strategies that address these challenges in QKD networks. In particular, we find that a proportional fairness pumping strategy (PF-PS) stands out by dynamically prioritizing users with lower average secret key rates and optimally balancing fairness with throughput. The proposed algorithm is a natural extension to quantum networks of the Proportional Fair Scheduler deployed in 4G LTE and 5G mobile networks. Both theoretical analysis and numerical simulations confirm that PF-PS is optimal for entangled state distribution, and thus, when adapted appropriately, proportional fair pumping is a strong candidate for efficient resource allocation in quantum networks.