Entanglement Percolation in Two Types of Irregular Quantum Networks

Abstract The issue of entanglement percolation in irregular quantum networks aims to investigate how to effectively transmit and maintain entanglement resources within complex network structures. This study is based on a deterministic entanglement transmission scheme and combines star-mesh transform, analyzing the entanglement percolation threshold and saturation points in two types of irregular networks through numerical simulation. The research results indicate that, with a certain level of precision, we calculate approximate values for the entanglement percolation threshold and saturation point between two given distant nodes on the butterfly network. Furthermore, for parallel-then-series networks, we derive a general analytical expression for determining the saturation point, which can be used to predict the saturation point of such networks under different numbers of nodes and different numbers of entangled resource states between adjacent nodes. Additionally, Comparing the concurrence percolation and the CEP based on the butterfly network and the parallel-then-series network, we find that the concurrence percolation indeed exhibits quantum superiority. These results provide specific numerical references and theoretical support for optimizing the entanglement transmission of these two types of irregular quantum networks.