Negativity Percolation in Continuous-Variable Quantum Networks

TL;DR

This paper introduces a new entanglement percolation theory for continuous-variable quantum networks, revealing a mixed-order phase transition and critical vulnerabilities that are distinct from discrete-variable systems.

Contribution

It develops a Gaussian-to-Gaussian entanglement distribution scheme and uncovers negativity percolation theory with unique critical phenomena in CV quantum networks.

Findings

Negativity percolation exhibits a mixed-order phase transition.

CV QNs belong to a new universality class, different from DV systems.

Critical vulnerabilities affect feedback stabilization near the transition threshold.

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.