Contact order governs the onset of entanglement cascades
Abstract
Entangling rates describe a direct entangling channel, but give no information when that channel is forbidden. For finite-dimensional analytic pure-state dynamics, we show that the onset of genuine (n+1)-partite entanglement is determined by the contact order m⋆ between the physical trajectory and the S|E product manifold. It is the first Taylor order that cannot be reproduced by any product curve, or equivalently the first nonvanishing order of the Fubini--Study distance from the product manifold. We derive a time-ordered recursion that removes curvature-induced kinematic terms and computes m⋆ from the Taylor coefficients of H(t). This provides a geometric description of an entanglement cascade, in which new subsystems can join multipartite entanglement only after one or more interaction steps. A symmetry-protected three-qubit model realizes m⋆=2, and a three-mode bosonic example shows that genuine tripartite entanglement can arise even when the two newly formed reduced pairs remain separable.
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BibTeX
@misc{kanno2026contact,
title = {{Contact order governs the onset of entanglement cascades}},
author = {Sugumi Kanno and Jiro Soda},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.06675},
eprint = {2609.06675},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.06675},
}
RIS
TY - UNPB
TI - Contact order governs the onset of entanglement cascades
AU - Sugumi Kanno
AU - Jiro Soda
PY - 2026
DA - 2026/09/06
PB - arXiv
DO - 10.48550/arxiv.2609.06675
UR - https://arxiv.org/abs/2609.06675
AB - Entangling rates describe a direct entangling channel, but give no information when that channel is forbidden. For finite-dimensional analytic pure-state dynamics, we show that the onset of genuine (n+1)-partite entanglement is determined by the contact order m_⋆ between the physical trajectory and the S|E product manifold. It is the first Taylor order that cannot be reproduced by any product curve, or equivalently the first nonvanishing order of the Fubini--Study distance from the product manifold. We derive a time-ordered recursion that removes curvature-induced kinematic terms and computes m_⋆ from the Taylor coefficients of H(t). This provides a geometric description of an entanglement cascade, in which new subsystems can join multipartite entanglement only after one or more interaction steps. A symmetry-protected three-qubit model realizes m_⋆=2, and a three-mode bosonic example shows that genuine tripartite entanglement can arise even when the two newly formed reduced pairs remain separable.
ER -