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arXiv:2411.11961 · Progress of Theoretical and Experimental Physics

A New Genuine Multipartite Entanglement Measure: from Qubits to Multiboundary Wormholes

Jaydeep Kumar Basak, Vinay Malvimat, Junggi Yoon

Published Jul 6, 2026• 0 citations
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Abstract

Abstract We introduce the latent entropy (L-entropy) as a novel measure to characterize the genuine multipartite entanglement in quantum systems. Our measure leverages the upper bound of reflected entropy and its maximal values attained by 2-uniform states for n-party ($n= 4,5$) and by the GHZ state for 3-party quantum systems. We demonstrate that the measure is a nonnegative, local unitary invariant function that vanishes for separable states. We then analyze its interesting characteristics in spin chain models and the Sachdev–Ye–Kitaev (SYK) model. Subsequently, we explore its implications for holography by deriving a Page-like curve for the L-entropy in the conformal field theory (CFT) dual to a multiboundary wormhole model. Furthermore, we examine the behavior of L-entropy in Haar random states, deriving analytical expressions and validating them against numerical results. In particular, we show that for $n =5$, random states approximate 2-uniform states with maximal multipartite entanglement. Furthermore, we propose a potential connection between random states and multiboundary wormhole geometries. Extending to finite-temperature systems, we introduce the multipartite thermal pure quantum (MTPQ) state, a multipartite generalization of the thermal pure quantum state, and explore its entanglement properties. By incorporating the state-dependent construction of the MTPQ state, we resolve the factorization issue in the random average of the MTPQ state, ensuring consistency with the correlation functions in the holographic dual multiboundary wormhole. Finally, we apply this construction to the multicopy SYK model and examine its multipartite entanglement structure.

DOI
10.1093/ptep/ptag131

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Abstract We introduce the latent entropy (L-entropy) as a novel measure to characterize the genuine multipartite entanglement in quantum systems. Our measure leverages the upper bound of reflected entropy and its maximal values attained by 2-uniform states for n-party (n=4,5n= 4,5n=4,5) and by the GHZ state for 3-party quantum systems. We demonstrate that the measure is a nonnegative, local unitary invariant function that vanishes for separable states. We then analyze its interesting characteristics in spin chain models and the Sachdev–Ye–Kitaev (SYK) model. Subsequently, we explore its implications for holography by deriving a Page-like curve for the L-entropy in the conformal field theory (CFT) dual to a multiboundary wormhole model. Furthermore, we examine the behavior of L-entropy in Haar random states, deriving analytical expressions and validating them against numerical results. In particular, we show that for n=5n =5n=5, random states approximate 2-uniform states with maximal multipartite entanglement. Furthermore, we propose a potential connection between random states and multiboundary wormhole geometries. Extending to finite-temperature systems, we introduce the multipartite thermal pure quantum (MTPQ) state, a multipartite generalization of the thermal pure quantum state, and explore its entanglement properties. By incorporating the state-dependent construction of the MTPQ state, we resolve the factorization issue in the random average of the MTPQ state, ensuring consistency with the correlation functions in the holographic dual multiboundary wormhole. Finally, we apply this construction to the multicopy SYK model and examine its multipartite entanglement structure.
We advance ``Latent entropy" (L-entropy) as a novel measure to characterize genuine multipartite entanglement in pure states, applicable to quantum systems with both finite and infinite degrees of freedom. This measure, derived from an upper bound on reflected entropy, attains its maximum for three-party GHZ states and n=4,5n=4,5n=4,5-party 222-uniform states. We establish that it satisfies all essential properties of a genuine multipartite entanglement measure, including being a pure-state entanglement monotone. We further obtain an analogue of the Page curve by analyzing the behavior of L-entropy in multiboundary wormholes, emphasizing their connection to multipartite entanglement in random states. Specifically, for n=5n = 5n=5, we show that random states approximate 222-uniform states, exhibiting maximal multipartite entanglement. Extending these ideas to finite temperatures, we introduce the Multipartite Thermal Pure Quantum (MTPQ) state, a generalization of the thermal pure quantum state to multipartite systems, and demonstrate that the entanglement structure in states of the multicopy SYK model exhibits finite-temperature 222-uniform behavior.
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 nnn-party quantum systems. Generalized L-entropy provides a natural ordering among kkk-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 nnn-party Haar-random states and demonstrate that, in the large local-dimension limit, the maximal L-entropy saturates its upper bound for odd nnn, while for even nnn 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 SYK4_44​, SYK2_22​, mass-deformed SYK, sparse SYK, and N=2\mathcal{N}=2N=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.
Black hole as a multipartite entangler: multi-entropy in AdS3{}_33​/CFT2{}_22​
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Multipartite entanglement is the premier resource for quantum technologies. Yet, its exact quantification in the laboratory is notoriously challenging, typically requiring the full knowledge of high dimensional quantum states. Here, we construct observable bounds to multipartite entanglement for systems of arbitrary size, which are functions of the local and global state purities, and correlation functions. First, we derive experimentally accessible upper and lower limits to both the bipartite entanglement of formation and the squashed entanglement of bipartite systems, by leveraging cornerstone results of quantum information theory: the entropy strong subadditivity inequality and the Koashi-Winter monogamy relation. Then, we convert them into bounds to the entanglement up to degree k for arbitrary states, and to the genuine k-partite entanglement, by employing a recently proposed method. Finally, we analytically and numerically test these results, by bounding the multipartite entanglement of several relevant states and mixtures, including the important classes of GHZ, Dicke, W states, and random pure states.
Entanglement is one of the most important concepts in quantum physics. We review recent progress in understanding the quantum entanglement in many-body systems using large- N solvable models: the Sachdev—Ye—Kitaev (SYK) model and its generalizations. We present the study of entanglement entropy in the original SYK model using three different approaches: the exact diagonalization, the eigenstate thermalization hypothesis, and the path-integral representation. For coupled SYK models, the entanglement entropy shows linear growth and saturation at the thermal value. The saturation is related to replica wormholes in gravity. Finally, we consider the steady-state entanglement entropy of quantum many-body systems under repeated measurements. The traditional symmetry breaking in the enlarged replica space leads to the measurement-induced entanglement phase transition.
Abstract We study the entanglement structure of states dual to multiboundary wormhole geometries using tensor network models. Perfect and random tensor networks tiling the hyperbolic plane have been shown to provide good models of the entanglement structure in holography. We extend this by quotienting the plane by discrete isometries to obtain models of the multiboundary states. We show that there are networks where the entanglement structure is purely bipartite, extending results obtained in the large temperature limit. We analyse the entanglement structure in a range of examples.