The Quantum Internet: A Complex Network Perspective

Abstract

The distribution of entanglement over large distances is fundamentally limited by optical fibre attenuation, necessitating quantum repeaters to realise a global quantum internet. While current theoretical studies often consider repeater performance in linear chains, these models do not capture the more complex topologies of spatially distributed communication networks. In this work, entanglement distribution is simulated across spatially embedded complex networks using a sequential repeater scheduling strategy and a realistic, hardware-aware model based on Nitrogen-Vacancy Centres. The dependence of network performance on spatial node density is first investigated. By applying an elementary link entanglement generation threshold, a percolation transition is identified, determining the critical density at which macroscopic entanglement connectivity emerges. End-to-end entanglement generation rate and fidelity are then analysed to characterise the physical capabilities of the network. Quantum key distribution is subsequently evaluated as a direct application of this distributed entanglement. By analysing the end-to-end secret key rate and network reachability, the operational 90%-reachability density required to establish macroscopic secure communication is determined. Ultimately, the results demonstrate that increasing the spatial density significantly enhances both the fidelity of the distributed entanglement and the resulting cryptographic key rates. Furthermore, the inclusion of multiplexing is shown to provide a substantial advantage across all metrics; it not only increases communication rates, but also dramatically lowers the density thresholds required to achieve both entanglement connectivity and end-to-end security