Unveiling the Importance of Nonshortest Paths in Quantum Networks

TL;DR

This paper investigates how non-shortest paths contribute to the enhanced connectivity in quantum networks, revealing that their abundance significantly improves network resilience and connectivity beyond classical predictions.

Contribution

It introduces a statistical physics model to analytically control path connectivity in hierarchical scale-free networks, distinguishing quantum from classical percolation universality classes.

Findings

Concurrence percolation is sensitive to non-shortest paths.

Quantum networks show higher resilience due to non-shortest paths.

Real-world networks exhibit similar enhanced connectivity effects.

Abstract

Quantum networks (QNs) exhibit stronger connectivity than predicted by classical percolation, yet the origin of this phenomenon remains unexplored. We apply a statistical physics model -- concurrence percolation -- to uncover the origin of stronger connectivity on hierarchical scale-free networks, the ($U,V$) flowers. These networks allow full analytical control over path connectivity through two adjustable path-length parameters, $U \leq V$. This precise control enables us to determine critical exponents well beyond current simulation limits, revealing that classical and concurrence percolations, while both satisfying the hyperscaling relation, fall into distinct universality classes. This distinction arises from how they "superpose" parallel, non-shortest path contributions into overall connectivity. Concurrence percolation, unlike its classical counterpart, is sensitive to non-shortest paths and shows higher resilience to detours as these paths lengthen. This enhanced resilience is also observed in real-world hierarchical, scale-free Internet networks. Our findings highlight a crucial principle for QN design: when non-shortest paths are abundant, they notably enhance QN connectivity beyond what is achievable with classical percolation.