Entanglement Routing and Bottlenecks in Grid Networks

In a recent article, Hahn et al. (npj Quantum Inf. 5, 76 (2019)) proposed a protocol for establishing EPR pairs in quantum networks. They used graph theoretic tools like local complementation and showed that their protocol can reduce the number of measurements required compared to standard repeater-based schemes for the same task. They also showed how local complementation can solve bottleneck issues in network architectures like the butterfly network. Here we extend their work, increasing its efficiency and the domain of applicability. Specifically, we show how the original proof can be modified to incorporate a wider variety of scenarios and provide examples demonstrating the modified protocol's advantage. Furthermore, we provide a method to apply recent results on bottlenecks in ring graphs to illustrate how grid graphs are affected. Using this, we demonstrate how the butterfly and similar networks suffer from the same bottleneck issues as ring and line graphs.Comment: An efficient protocol for establishing EPR pairs in quantum networks is proposed by generalizing the work of Hahn et al. (npj Quantum Inf. 5, 76 (2019)