Topology and density control of satellite-defined photonic quantum networks

Creating photonic quantum networks by distributing entangled photon pairs through low Earth orbit satellites is a promising technological advance. A recent work has studied a model of such networks and reported the presence of a heavy-tailed degree distribution. This heterogeneous structure is highly undesirable when it comes to the quantum memory utilization efficiency and network robustness under malicious attack. In this work, however, we show that such a topology is not necessarily inherent to satellite-based quantum networks. We theoretically analyze factors that determine the connection probability between two nodes and propose a principled design methodology to control both the topology and density of the resulting network. We present numerical evidence that our method can continuously transform the heterogeneous heavy-tailed network into a more homogeneous Erdős-Rényi-like random network with the prescribed level of density as characterized by the average or maximal degree. Such results are in good agreement with our theoretical analysis, which not only predicts the qualitative structural transition but also provides a quantitative way to estimate important network features during the process. Under our control strategies, the resulting network can achieve various desirable properties, such as a short path length and diameter, high quantum memory utilization efficiency, and enhanced robustness against attack. We believe the design principle proposed in this work represents an important step towards building and controlling functionally efficient satellite-photonic quantum networks in the future.