Probing the Hierarchy of Genuine Multipartite Entanglement with Generalized Latent Entropy

• URL: http://arxiv.org/abs/2510.19922v1
• Date: Wed, 22 Oct 2025 18:00:04 GMT
• Title: Probing the Hierarchy of Genuine Multipartite Entanglement with Generalized Latent Entropy
• Authors: Byoungjoon Ahn, Jaydeep Kumar Basak, Keun-Young Kim, Gwon Bin Koo, Vinay Malvimat, Junggi Yoon,
• Abstract summary: Generalized L-entropy (L-entropy) is a measure of genuine multipartite entanglement in pure states of $n$-party quantum systems.<n>We show that L-entropy serves as a sensitive probe of multipartite entanglement, revealing how deformations influence quantum entanglement structure in strongly interacting systems.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We introduce generalization of the recently proposed Latent Entropy (L-entropy) [1] as a refined measure of genuine multipartite entanglement (GME) in pure states of $n$-party quantum systems. Generalized L-entropy satisfies the axioms required for a valid GME measure and provides a natural ordering among $k$-uniform states maximizing 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. 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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