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arXiv:2610.11921

Multipartite Entanglement Geometry in AdS/BCFT

Debarshi Basu, Qiang Wen, Mingshuai Xu

Published Oct 8, 2026• 0 citations
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Abstract

Multipartite entanglement measures probe how quantum correlations are organized beyond what can be inferred from pairwise entropies. We study how this structure is reshaped by a physical boundary in a holographic BCFT. The end-of-the-world brane opens new relative-homology channels for multipartite entanglement, allowing connected bulk webs to reorganize and factorize at scales that need not coincide with any ordinary Ryu--Takayanagi transition. In static AdS$_3$/BCFT$_2$, this produces a characteristic hierarchy of multipartite phases and a nontrivial dependence of genuine multi-entropy on the boundary. In the thermofield-double state, genuinely connected webs can instead be supported through the Einstein--Rosen bridge, leading to growth, reconnection and saturation scales distinct from the usual Hartman--Maldacena transitions. These results show that multipartite entanglement is sensitive not only to extremal-surface areas but also to how bulk entanglement structures are allowed to join, split and terminate in the presence of a boundary.

DOI
10.48550/arxiv.2610.11921

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Multipartite entanglement measures probe how quantum correlations are organized beyond what can be inferred from pairwise entropies. We study how this structure is reshaped by a physical boundary in a holographic BCFT. The end-of-the-world brane opens new relative-homology channels for multipartite entanglement, allowing connected bulk webs to reorganize and factorize at scales that need not coincide with any ordinary Ryu--Takayanagi transition. In static AdS3_33​/BCFT2_22​, this produces a characteristic hierarchy of multipartite phases and a nontrivial dependence of genuine multi-entropy on the boundary. In the thermofield-double state, genuinely connected webs can instead be supported through the Einstein--Rosen bridge, leading to growth, reconnection and saturation scales distinct from the usual Hartman--Maldacena transitions. These results show that multipartite entanglement is sensitive not only to extremal-surface areas but also to how bulk entanglement structures are allowed to join, split and terminate in the presence of a boundary.
Black hole as a multipartite entangler: multi-entropy in AdS3{}_33​/CFT2{}_22​
We study multipartite entanglement in typical pure states holographically dual to pure BTZ black holes, using multi-entropy and its ``genuine'' version. In the bulk, these quantities are computed by minimal geodesic networks (so-called Steiner trees). We find that at sufficiently high temperature, the genuine tripartite multi-entropy exhibits a volume-law scaling in sharp contrast to vacuum AdS3_33​, where the genuine contribution is universal and size-independent. Moreover, we find another phase: once one subsystem exceeds half of the total system, the leading genuine tripartite entanglement vanishes and reduces to that for global AdS3{}_33​. This transition is indeed consistent with recent arguments for distillable EPR pairs in tripartite Haar-random states. Motivated by finite-cutoff holography, we further study the radial cutoff dependence of multi-entropy and show that genuine multi-entropy acquires nontrivial size dependence even for the tripartite case in AdS3{}_33​. As a byproduct, we also observe an intriguing ``area-law'' contribution to multi-entropy that is relevant to vacuum AdS3{}_33​.
Abstract In this study, we extend the surface growth approach for bulk reconstruction into the AdS spacetime with a boundary in the AdS/BCFT correspondence. We show that the geometry in the entanglement wedge with a boundary can be constructed from the direct growth of bulk extremal surfaces layer by layer. Furthermore, we observe that the surface growth configuration in BCFT can be connected with the defect multi scale entanglement renormalization ansatz (MERA) tensor network. Additionally, we investigate the entanglement of purification within the surface growth process, which not only reveals more refined structure of entanglement entropy in the entanglement wedge but also suggests a selection rule for surface growth in the bulk reconstruction.
A bstract We investigate how IR modifications of the bulk geometry reshape long-range multipartite entanglement on the boundary in holography. We modify the IR geometries in two opposite directions: spherical modifications that enhance long-range entanglement and hyperbolic modifications that suppress them. We utilize various multipartite entanglement measures/signals to analyze the multipartite entanglement structures. These measures/signals are combinations of entanglement entropy, multi-entropy, entanglement wedge cross sections (EWCS) and multi-EWCS. Our results reveal that in the extremal limits of these two geometric modifications, the multipartite entanglement structures exhibit starkly contrasting behaviors: various measures saturate either their theoretical upper or lower bounds in the respective geometries. This demonstrates that IR deformations provide a practical holographic framework for realizing extremal entanglement regimes. Moreover, it serves as an effective tool for studying quantum marginal problems in holography. Finally, by observing how different measures respond to these engineered geometries, we gain clarifying insights into the specific types of multipartite entanglement that each measure/signal is particularly sensitive to.
A bstract We study how multipartite entanglement is dynamically reorganized during holographic thermalization following a global quench in AdS 3 /CFT 2 . We first use the n -partite information (− 1) n I n to probe collective multipartite entanglement in holographic configurations where the full n -region entanglement wedge is connected while all fewer-party ones are disconnected, thereby excluding fewer-party contributions. The spatial range of multipartite entanglement first expands and then contracts as the system approaches its late-time locally thermal state. Entanglement involving different numbers of parties develops on comparable early-time scales, while the entanglement that involves more parties relaxes more slowly, revealing a transient propagation from shorter to longer spatial distances. We further compute the Markov gap and the genuine tripartite multi-entropy as complementary probes of tripartite entanglement. The Markov gap can remain enhanced after local thermalization, whereas the genuine tripartite multi-entropy undergoes a nonmonotonic evolution and returns to its vacuum value for the adjacent tripartition considered in this work. These results show that a global quench redistributes the entanglement across spatial scales and reorganizes its multipartite structure.
In a companion paper, we found that near the untwisted point of a four-boundary AdS3_33​ wormhole, whenever the complete bipartite Ryu-Takayanagi entropy vector is insensitive to a Fenchel-Nielsen twist, the holographic q=4\mathtt q=4q=4 multi-entropy is insensitive as well. Here we show that the situation changes at finite twist. The twist lengthens the crossing geodesics and thereby enlarges the region in which all bipartite RT entropies remain invariant. In part of this enlarged region, a twist-sensitive q=4\mathtt q=4q=4 network becomes globally minimal. We thus find an open region of wormhole moduli space in which the complete bipartite RT entropy vector is exactly unchanged while the q=4\mathtt q=4q=4 multi-entropy detects the twist. Our result provides an explicit example in which the q=4\mathtt q=4q=4 genuine multi-entropy probes bulk geometric information invisible to all bipartite entanglement entropies.
We investigate how the junction law for multipartite entanglement is realized in confining holographic backgrounds, using genuine multi-entropy (GM) as our main diagnostic. We first study an AdS3_33​ hard-wall toy model as an analytic benchmark, where multi-way cuts and junction geometries can be analyzed explicitly. In this setup, we classify the relevant saddles, determine the dominant phases, and show that the genuinely multipartite contribution diagnosed by GM is localized near the junction. We also examine how this structure depends on subsystem sizes, asymmetry, and the confinement scale, including phase transitions between competing saddles. We then move beyond the hard-wall benchmark to smooth confining geometries, focusing on the D4-soliton and D3-soliton backgrounds and formulating the corresponding framework also for the Klebanov--Strassler background. In the smooth-cap examples, we find that the junction picture persists, while the detailed phase structure differs from the hard-wall case: in particular, the hard-wall plateau does not survive, and GM instead decreases monotonically and vanishes at a finite critical scale. We also find that the short-distance behavior is background-dependent, with GM(3)∼L−4\mathrm{GM}^{(3)}\sim L^{-4}GM(3)∼L−4 in the D4-soliton background, GM(3)∼L−2\mathrm{GM}^{(3)}\sim L^{-2}GM(3)∼L−2 in the D3-soliton background, and GM(3)∼L−2⋅(log⁡L)2\mathrm{GM}^{(3)}\sim L^{-2}\cdot (\log L)^{2}GM(3)∼L−2⋅(logL)2 in the Klebanov--Strassler background. These results clarify which features of the junction-law picture are robust in confining holography and which features of the phase structure and short-distance scaling are background-dependent.