A Mixed-Order Phase Transition in Continuous-Variable Quantum Networks

• URL: http://arxiv.org/abs/2507.16417v1
• Date: Tue, 22 Jul 2025 10:09:21 GMT
• Title: A Mixed-Order Phase Transition in Continuous-Variable Quantum Networks
• Authors: Yaqi Zhao, Kan He, Yongtao Zhang, Jinchuan Hou, Jianxi Gao, Shlomo Havlin, Xiangyi Meng,
• Abstract summary: Quantum networks (QNs) have been predominantly driven by discrete-variable (DV) architectures.<n>We present a new form of entanglement percolation--negativity percolation theory (NegPT)<n>We show 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.
• Score: 1.3946421495394776
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum networks (QNs) have been predominantly driven by discrete-variable (DV) architectures. Yet, many 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 conceptual 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 not only unify statistical models for CV-based entanglement distribution but also 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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