Distinguishing universality classes of two entanglement percolation protocols
Phys. Rev. A 114, 022452 – Published 24 August, 2026
DOI: https://doi.org/10.1103/pxnm-pddm
Abstract
Various entanglement percolation protocols provide distinct statistical-physics frameworks for analyzing the capability of quantum networks (QNs) to achieve long-distance entanglement distribution. The percolation efficiencies and critical exponents exhibited by different existing protocols vary considerably, necessitating a classification of these numerous protocols. This raises an urgent question: From the perspectives of both statistical physics and practical guidance for QNs, do these protocols belong to the same or different universality classes? To date, only the classical entanglement percolation protocol [Acín et al., Nat. Phys. 3, 256 (2007)] and the pure-state concurrence percolation protocol [Meng et al., Phys. Rev. Lett. 126, 170501 (2021)] have been confirmed to belong to distinct universality classes, as demonstrated in [Hu et al., Sci. Adv. 11, eadt2404 (2025)]. In this paper we prove that the pure-state and mixed-state concurrence percolation protocols [Wang et al., Commun. Phys. 9, 28 (2026)] fall into different universality classes. We compute critical exponents for several QN topologies, including flowers and two-dimensional lattices. Our results show that the two concurrence percolation protocols exhibit different sets of critical exponents. This demonstrates that the two protocols belong to different universality classes, revealing that the macroscopic connectivity of QNs is governed not only by network topologies but also, fundamentally, by the type of underlying resource states. From the perspective of designing QNs, our results exhibit distinct entanglement transmission capabilities for different protocols: The larger the critical exponent, the stronger the entanglement transmission capability, which directly impacts the design of QNs for achieving long-range entanglement distribution.