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arXiv · 2510.19922

Probing the Hierarchy of Genuine Multipartite Entanglement with Generalized Latent Entropy

Byoungjoon Ahn·Jaydeep Kumar Basak·Keun-Young Kim·Gwon Bin Koo·Vinay Malvimat·Junggi Yoon
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Abstract

We introduce generalization of the recently proposed \textit{Latent Entropy} (L-entropy) \cite{Basak:2024uwc} as a refined measure of genuine multipartite entanglement (GME) in pure states of $n$-party quantum systems. Generalized L-entropy provides a natural ordering among $k$-uniform states, maximising for absolutely maximally entangled states (AME), effectively capturing the hierarchical structure of multipartite entanglement. We analyze the behavior of this measure for $n$-party Haar-random states and demonstrate that, in the large local-dimension limit, the maximal L-entropy saturates its upper bound for odd $n$, while for even $n$ it approaches the bound asymptotically. Furthermore, we apply this framework to examine multipartite entanglement properties of quantum states in several variants of the Sachdev-Ye-Kitaev (SYK) model, including SYK$_4$, SYK$_2$, mass-deformed SYK, sparse SYK, and $\mathcal{N}=2$ supersymmetric SYK model. The results demonstrate that the generalized L-entropy serves as a sensitive probe of multipartite entanglement, revealing how deformations influence quantum entanglement structure in such strongly interacting systems.

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Byoungjoon Ahn, Jaydeep Kumar Basak, Keun-Young Kim, Gwon Bin Koo, Vinay Malvimat, Junggi Yoon. 2025-10-22. Probing the Hierarchy of Genuine Multipartite Entanglement with Generalized Latent Entropy. https://arxiv.org/abs/2510.19922

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