Concurrence Percolation Behavior in Diluted Quantum Networks

The evolution of connectivity in quantum networks under decoherence and link degradation is a central problem in quantum information, calling for further understanding of the nature of its transition during structural network degradation. By diluting each link with probability 1−f, we focus on connectivity strength transitions in diluted hierarchical scale-free quantum networks, the (u,v) flowers, which are analytically tractable through two adjustable path-length parameters, u≤v. Incorporating quantum concurrence percolation and comparing it with classical percolation, we analyze the transitions of critical thresholds for various values of f and v from analytical, numerical, and simulation perspectives. The results demonstrate that quantum percolation exhibits consistently lower critical thresholds than classical percolation, even under various topologies and dilution levels. Our work implies that quantum multipath entanglement provides an intrinsic compensatory mechanism against structural degradation and that the hierarchical scale-free topology contributes to the failure resistance and robustness of quantum networks with multipath coupling.