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arXiv · 2510.18408

Multi-entropy from Linking in Chern-Simons Theory

Ma-Ke Yuan·Mingyi Li·Yang Zhou
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Abstract

We study the multipartite entanglement structure of quantum states prepared by the Euclidean path integral over three-manifolds with multiple torus boundaries (the so-called link states) in both Abelian and non-Abelian Chern-Simons theories. For three-component link states in the Abelian theory, we derive an explicit formula for the R\'enyi multi-entropy in terms of linking numbers. We further show that the genuine multi-entropy faithfully quantifies the tripartite entanglement generated by GHZ-states, consistent with the fact that the prepared states are stabilizer states.

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Ma-Ke Yuan, Mingyi Li, Yang Zhou. 2025-10-21. Multi-entropy from Linking in Chern-Simons Theory. https://doi.org/10.1007/jhep09(2026)010

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