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arXiv:2609.37394

Can Multipartite Entanglement Probe Wormhole Moduli Invisible to Bipartite Entanglement?

Norihiro Iizuka

Published Sep 29, 2026• 0 citations
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Abstract

We ask whether multipartite entanglement can probe bulk moduli invisible to bipartite entanglement. We study this question in an explicit family of four-boundary AdS$_3$ wormholes related by a Fenchel-Nielsen twist $τ$, asking whether the complete set of bipartite RT entropies can remain exactly $τ$-independent while the holographic $\mathtt q=4$ multi-entropy is sensitive to the twist. Within the class of configurations analyzed here, for sufficiently small $|τ|$, we find no such regime along the symmetric line $\ell=m$: the globally minimal $\mathtt q=4$ network is itself exactly $τ$-independent throughout the parameter range analyzed. This conclusion is not a priori obvious: it emerges from a competition among several admissible configurations whose relative ordering changes multiple times as the geometry is varied, and persists up to the point where the bipartite RT entropies themselves become twist-sensitive.

DOI
10.48550/arxiv.2609.37394

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Multipartite Entanglement Can Probe Wormhole Moduli Invisible to Bipartite Entanglement

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In a companion paper, we found that near the untwisted point of a four-boundary AdS$_3$ wormhole, whenever the complete bipartite Ryu-Takayanagi entropy vector is insensitive to a Fenchel-Nielsen twist, the holographic $\mathtt q=4$ 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 $\mathtt q=4$ 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 $\mathtt q=4$ multi-entropy detects the twist. Our result provides an explicit example in which the $\mathtt q=4$ genuine multi-entropy probes bulk geometric information invisible to all bipartite entanglement entropies.

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We ask whether multipartite entanglement can probe bulk moduli invisible to bipartite entanglement. We study this question in an explicit family of four-boundary AdS3_33​ wormholes related by a Fenchel-Nielsen twist τττ, asking whether the complete set of bipartite RT entropies can remain exactly τττ-independent while the holographic q=4\mathtt q=4q=4 multi-entropy is sensitive to the twist. Within the class of configurations analyzed here, for sufficiently small ∣τ∣|τ|∣τ∣, we find no such regime along the symmetric line ℓ=m\ell=mℓ=m: the globally minimal q=4\mathtt q=4q=4 network is itself exactly τττ-independent throughout the parameter range analyzed. This conclusion is not a priori obvious: it emerges from a competition among several admissible configurations whose relative ordering changes multiple times as the geometry is varied, and persists up to the point where the bipartite RT entropies themselves become twist-sensitive.
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.
The AdS/CFT correspondence relates quantum entanglement between boundary Conformal Field Theories and geometric connections in the dual asymptotically Anti-de Sitter space-time. We consider entangled states in the n-fold tensor product of a 1+1 dimensional CFT Hilbert space defined by the Euclidean path integral over a Riemann surface with n holes. In one region of moduli space, the dual bulk state is a black hole with n asymptotically AdS_3 regions connected by a common wormhole, while in other regions the bulk fragments into disconnected components. We study the entanglement structure and compute the wave function explicitly in the puncture limit of the Riemann surface in terms of CFT n-point functions. We also use AdS minimal surfaces to measure entanglement more generally. In some regions of the moduli space the entanglement is entirely multipartite, though not of the GHZ type. However, even when the bulk is completely connected, in some regions of the moduli space the entanglement is almost entirely bipartite: significant entanglement occurs only between pairs of CFTs. We develop new tools to analyze intrinsically n-partite entanglement, and use these to show that for some wormholes with n similar sized horizons there is intrinsic entanglement between at least n-1 parties, and that the distillable entanglement between the asymptotic regions is at least (n+1)/2 partite.
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​.
The AdS/CFT correspondence relates quantum entanglement between boundary conformal field theories and geometric connections in the dual asymptotically anti-de Sitter spacetime. We consider entangled states in the n-fold tensor product of a 1 + 1 dimensional CFT Hilbert space defined by the Euclidean path integral over a Riemann surface with n holes. In one region of moduli space, the dual bulk state is a black hole with n asymptotically AdS3 regions connected by a common wormhole, while in other regions the bulk fragments into disconnected components. We study the entanglement structure and compute the wave function explicitly in the puncture limit of the Riemann surface in terms of CFT n-point functions. We also use AdS minimal surfaces to measure entanglement more generally. In some regions of the moduli space the entanglement is entirely multipartite, though not of the GHZ type. However, even when the bulk is completely connected, there are regions of the moduli space in which the entanglement is instead almost entirely bipartite: significant entanglement occurs only between pairs of CFTs. We develop new tools to analyze intrinsically n-partite entanglement, and use these to show that for some wormholes with n similar sized horizons there is intrinsic entanglement between all n parties, and that the distillable entanglement between the asymptotic regions is at least (n + 1)/2 partite.
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.
Abstract We analyze the 1+1 CFT states dual to hot (time-symmetric) 2+1 multiboundary AdS wormholes. These are black hole geometries with high local temperature, asymptotically-AdS 3 regions, and arbitrary internal topology. The dual state at t = 0 is defined on n circles. We show these to be well-described by sewing together tensor networks corresponding to thermofield double states. As a result, the entanglement is spatially localized and bipartite: away from particular boundary points (‘vertices’) any small connected region A of the boundary CFT is entangled only with another small connected region B , where B may lie on a different circle or may be a different part of the same circle. We focus on the pair-of-pants case, from which more general cases may be constructed. We also discuss finite-temperature corrections, where we note that the states involve a code subspace in each circle.