Probing the Hierarchy of Genuine Multipartite Entanglement with Generalized Latent Entropy
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arXiv
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| Format: | Preprint |
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2025
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| author | Ahn, Byoungjoon Basak, Jaydeep Kumar Kim, Keun-Young Koo, Gwon Bin Malvimat, Vinay Yoon, Junggi |
| author_facet | Ahn, Byoungjoon Basak, Jaydeep Kumar Kim, Keun-Young Koo, Gwon Bin Malvimat, Vinay Yoon, Junggi |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_19922 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Probing the Hierarchy of Genuine Multipartite Entanglement with Generalized Latent Entropy Ahn, Byoungjoon Basak, Jaydeep Kumar Kim, Keun-Young Koo, Gwon Bin Malvimat, Vinay Yoon, Junggi High Energy Physics - Theory Quantum Physics 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. |
| title | Probing the Hierarchy of Genuine Multipartite Entanglement with Generalized Latent Entropy |
| topic | High Energy Physics - Theory Quantum Physics |
| url | https://arxiv.org/abs/2510.19922 |