Entanglement Dynamics in Katz-Weighted Graph States
Abstract
We investigate the entanglement dynamics of quantum states defined on graphs with non-local Ising interactions governed by the Katz kernel of the underlying network. The interaction pattern is physically motivated by a gapped fermionic mediator propagating on the same graph, whose perturbative elimination yields an effective Katz-weighted Ising Hamiltonian. Using the Entanglement Distance, we derive an exact analytical expression for the entanglement generated from an initially separable state and apply it to representative deterministic graph families. We then characterize the dynamics in different propagation regimes. In the weak-Katz regime, the dynamics admits a systematic motif expansion with triangles entering at first order order and four-cycles, local degree structure, and overlappin triangles appearing at second order. In the strong-propagation regime, the interaction is instead dominated by the principal adjacency mode and by the localization properties of its eigenvector. For Erdős--Rényi graphs, the weak-propagation expansion can be averaged analytically, revealing a locally tree-like contribution in the sparse regime and saturation of the Entanglement Distance density in the dense regime. Our results connect entanglement dynamics with both the walk-based and spectral structure of complex networks.
Related
- Hydrodynamic limit of exclusion processes with killing on weighted Riemannian manifolds via a graph discretization
- Weighted Score Matching on Bounded Domains: Nonparametric Density Estimation and Interaction Graph Recovery
- Entanglement of purification for Werner states: canonical purification and nonadditivity
- Entanglement Sudden Death in Gapped Ground States
- Exact Entanglement Swapping through Single-Occupancy Measurements in Gaussian Fermion States
BibTeX
@misc{simone2026entanglement,
title = {{Entanglement Dynamics in Katz-Weighted Graph States}},
author = {Lucio De Simone and Lorenzo Capra and Roberto Franzosi},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.20390},
eprint = {2609.20390},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.20390},
}
RIS
TY - UNPB
TI - Entanglement Dynamics in Katz-Weighted Graph States
AU - Lucio De Simone
AU - Lorenzo Capra
AU - Roberto Franzosi
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.20390
UR - https://arxiv.org/abs/2609.20390
AB - We investigate the entanglement dynamics of quantum states defined on graphs with non-local Ising interactions governed by the Katz kernel of the underlying network. The interaction pattern is physically motivated by a gapped fermionic mediator propagating on the same graph, whose perturbative elimination yields an effective Katz-weighted Ising Hamiltonian. Using the Entanglement Distance, we derive an exact analytical expression for the entanglement generated from an initially separable state and apply it to representative deterministic graph families. We then characterize the dynamics in different propagation regimes. In the weak-Katz regime, the dynamics admits a systematic motif expansion with triangles entering at first order order and four-cycles, local degree structure, and overlappin triangles appearing at second order. In the strong-propagation regime, the interaction is instead dominated by the principal adjacency mode and by the localization properties of its eigenvector. For Erdős--Rényi graphs, the weak-propagation expansion can be averaged analytically, revealing a locally tree-like contribution in the sparse regime and saturation of the Entanglement Distance density in the dense regime. Our results connect entanglement dynamics with both the walk-based and spectral structure of complex networks.
ER -