Unveiling the Importance of Longer Paths in Quantum Networks
- URL: http://arxiv.org/abs/2402.15462v1
- Date: Fri, 23 Feb 2024 17:45:00 GMT
- Title: Unveiling the Importance of Longer Paths in Quantum Networks
- Authors: Xinqi Hu, Gaogao Dong, Renaud Lambiotte, Kim Christensen, Jingfang
Fan, Lixin Tian, Shlomo Havlin, Xiangyi Meng
- Abstract summary: We explore the potential statistical theory underlying enhanced connectivity, known as concurrence percolation.
Our findings reveal a first principle for quantum network (QN) design: longer paths still contribute significantly to QN connectivity -- as long as they are abundant.
- Score: 0.3141085922386211
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: The advancement of quantum communication technologies is calling for a better
understanding of quantum network (QN) design from first principles, approached
through network science. Pioneering studies have established a classical
percolation mapping to model the task of entanglement transmission across QN.
Yet, this mapping does not capture the stronger, yet not fully understood
connectivity observed in QNs, which facilitates more efficient entanglement
transmission than predicted by classical percolation. In this work, we explore
the critical phenomena of the potential statistical theory underlying this
enhanced connectivity, known as concurrence percolation. Compared to classical
percolation, the concurrence percolation mapping employs a unique approach of
"superposing" path connectivities, utilizing a different set of path
connectivity rules, thereby boosting the overall network connectivity. Firstly,
we analytically derive the percolation critical exponents for hierarchical,
scale-free networks, particularly the UV flower model, characterized by two
distinct network length scales, U$\leq$V. Our analysis confirms that classical
and concurrence percolations, albeit both satisfying the hyperscaling relation,
fall into separate universality classes. Most importantly, this separation
stems from their different treatment of non-shortest path contributions to
overall connectivity. Notably, as the longer path scale V increases,
concurrence percolation retains unignorable dependence of both its critical
threshold and critical exponents on V and thus, comparing with its classical
counterpart, shows a higher resilience to the weakening of non-shortest paths.
This higher resilience is also observed in real-world network topology, e.g.,
the Internet. Our findings reveal a first principle for QN design: longer paths
still contribute significantly to QN connectivity -- as long as they are
abundant.
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