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arXiv · 2507.16417

Negativity Percolation in Continuous-Variable Quantum Networks

Yaqi Zhao·Kan He·Yongtao Zhang·Jinchuan Hou·Jianxi Gao·Shlomo Havlin·Xiangyi Meng
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Abstract

Quantum networks (QNs) have been predominantly driven by discrete-variable (DV) architectures. Yet, optical platforms naturally generate Gaussian states--the common states of continuous-variable (CV) systems, making CV-based QNs an attractive route toward scalable, chip-integrated quantum computation and communication. To bridge the gap between well-studied DV entanglement percolation theories and their CV counterpart, we introduce a Gaussian-to-Gaussian entanglement distribution scheme that deterministically transports two-mode squeezed vacuum states across large CV networks. Analysis of the scheme's collective behavior using statistical-physics methods reveals a new form of entanglement percolation--negativity percolation theory (NegPT)--characterized by a bounded entanglement measure called the ratio negativity. We discover that NegPT exhibits a mixed-order phase transition, marked simultaneously by both an abrupt change in global entanglement and a long-range correlation between nodes. This distinctive behavior places CV-based QNs in a new universality class, fundamentally distinct from DV systems. Additionally, the abruptness of this transition introduces a critical vulnerability of CV-based QNs: conventional feedback mechanism becomes inherently unstable near the threshold, highlighting practical implications for stabilizing large-scale CV-based QNs. Our results unify statistical models for CV-based entanglement distribution and uncover previously unexplored critical phenomena unique to CV systems, providing valuable insights and guidelines essential for developing robust, feedback-stabilized QNs.

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Yaqi Zhao, Kan He, Yongtao Zhang, Jinchuan Hou, Jianxi Gao, Shlomo Havlin, Xiangyi Meng. 2025-07-22. Negativity Percolation in Continuous-Variable Quantum Networks. https://arxiv.org/abs/2507.16417

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