arXiv subjects

Norihiro Iizuka

Publications and source records attributed to Norihiro Iizuka.

At least 19 recordsLinked to original sources

arXiv2026

Can Multipartite Entanglement Probe Wormhole Moduli Invisible to Bipartite Entanglement?

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.

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arXiv2026

Multipartite Entanglement Can Probe Wormhole Moduli Invisible to Bipartite Entanglement

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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arXiv2026

Genuine Multi-Entropy in Abelian Chern--Simons Theory: Exact Key-Ring Collapse and Its Breakdown for Generic Link States

We study genuine multi-entropy in Abelian $U(1)_k$ Chern-Simons theory. For key-ring link states, where only the linking numbers between one distinguished component $K$ and the remaining $\mathtt{q}-1$ components are nonzero, we derive an exact closed-form expression for the $\mathtt{q}$-partite Rényi multi-entropy for general $\mathtt{q}$, level $k$, and Rényi index $n$. For $\mathtt{q}=4$, this shows that the genuine multi-entropy $\mathrm{GM}^{(4)}_n$ collapses exactly onto the tripartite information $I_{3,n}$ for all $n$, while for $\mathtt{q}=5$ it is likewise completely determined, for all $n$, by a linear combination of tripartite and bipartite Rényi multi-entropies. We then go beyond the key-ring class and study general four-component link states with arbitrary pairwise linking numbers. A numerical scan over Chern--Simons levels $2\leq k\leq24$ shows that the all-$n$ collapse found analytically for key-ring states does not survive for generic link states. Remarkably, the collapse remains exact at $n=2$ for every level examined. At $n=3$, violations occur, within the scanned range, only when $3\mid k$, with a further dependence on the $3$-adic valuation of $k$. At $n=4$ and $n=5$, violations occur for every level examined, with rates that vary strongly with $k$. These results show that the breakdown is not controlled simply by the zero-divisor structure of composite $\mathbb Z_k$, but instead exhibits a nontrivial joint dependence on the Rényi index and the arithmetic structure of the Chern--Simons level.

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arXiv2026

Notes on the Graph-Encoded Manifolds for the (Genuine) Multi-Entropy

Genuine multi-entropy is the part of the $\mathtt{q}$-partite multi-entropy that captures entanglement genuinely shared among all $\mathtt{q}$ parties, rather than entanglement already present among fewer subsystems. It was recently proposed that this genuine part -- so-called a multipartite entanglement signal -- can be studied via the graph-encoded manifold (GEM) built from the underlying $\mathtt{q}$-partite multi-entropy permutation family: reading its $\mathtt{q}$-colored contraction graph $Γ_{\mathtt{q},n}$ as a triangulation by $(\mathtt{q}-1)$-simplices. Focusing on $\mathtt{q}=4$, we classify the topology of every vertex link of $Γ_{4,n}$ and find $χ_{\rm link}(n)=n(3-n)$: the graph satisfies the GEM condition, namely every vertex link is a two-sphere, if and only if $n=2$, while for every $n\geq3$ the vertex links are closed surfaces of strictly positive genus $g_n=\tfrac12(n-1)(n-2)$, so that the graph instead defines a simplicial complex with a conical singularity at every vertex.

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arXiv2026

Genuine Multi-Entropy in the Toric Code

We study genuine multi-entropy as a diagnostic of multipartite entanglement in the toric code, which provides a controlled setting for probing multipartite structures in topologically ordered states. Our main question is whether genuine multi-entropy captures information that is not reducible to conventional lower-party entropic data, such as topological entanglement entropy. We first analyze toric-code ground states that admit a stabilizer-state description, where the relevant quantities can be evaluated exactly. In this sector, genuine multi-entropy reflects the topological structure and symmetries of the toric code, while exhibiting highly constrained relations to lower-party multi-entropies. We conjecture that, for stabilizer states and ${q}\ge4$, the ${q}$-partite genuine multi-entropy at replica index $n<{q}$ collapses to a linear combination of multi-entropies involving at most ${q}-2$ parties. We establish this pattern explicitly for ${q}=4$ in the toric code stabilizer sector: for $n=2,3$, the genuine multi-entropy is proportional to the tripartite information $I_3$ and, for the Kitaev--Preskill partition, contains no independent genuine four-partite information beyond that captured by the topological entanglement entropy. At $n=4$, however, this reduction breaks down: the genuine multi-entropy is no longer proportional to $I_3$, but remains a topological invariant of the toric-code stabilizer ground states. For generic non-stabilizer superpositions within the ground-state manifold and for coherent superpositions of local excitations, the low-$n$ reduction also fails. These results show that genuine multi-entropy probes multipartite entanglement structure beyond the tripartite information, and hence beyond the topological entanglement entropy in the Kitaev--Preskill partition, whereas for stabilizer states at low replica index it reduces to lower-partite entropic data.

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arXiv2026

Structural Obstruction to Replica Symmetry Breaking for Multi-Entropy in Random Tensor Networks

We study replica symmetry breaking (RSB) for multi-entropy in the random-tensor-network (RTN) domain-wall spin model. Our main result is that, within this framework, multi-entropy has a structural obstruction to RSB for any Rényi index $n$ and any multipartite number $\mathtt{q}$. This obstruction arises because the boundary permutations relevant to multi-entropy are organized along mutually incompatible coordinate directions of the replica hypercube, and therefore do not admit a nontrivial common geodesic intermediate permutation $τ$ in the Cayley graph of $S_N$. This is in sharp contrast to entanglement negativity, which does admit such a $τ$-mediated saddle and exhibits RSB in the same framework. As a robustness check, we also consider a toy $\mathbb{Z}_2$ gauge extension of the spin model with a minimal bulk gauge constraint. Numerical evidence in this gauged model indicates that multi-entropy continues to show no sign of RSB at $n=2$ and $n=3$, while negativity continues to exhibit RSB. Our results show that, within the RTN spin-model description, multi-entropy is not "RSB-friendly'': its boundary data are structurally incompatible with a nontrivial common geodesic intermediate permutation, unlike negativity.

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arXiv2026

The Junction Law for Multipartite Entanglement in Confining Holographic Backgrounds

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 AdS$_3$ 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 $\mathrm{GM}^{(3)}\sim L^{-4}$ in the D4-soliton background, $\mathrm{GM}^{(3)}\sim L^{-2}$ in the D3-soliton background, and $\mathrm{GM}^{(3)}\sim L^{-2}\cdot (\log L)^{2}$ 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.

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arXiv2026

Where Multipartite Entanglement Localizes: The Junction Law for Genuine Multi-Entropy

We uncover a "junction law" for genuine multipartite entanglement, suggesting that in gapped local systems multipartite entanglement is controlled and effectively localized near junctions where subsystem boundaries meet. Using the Rényi-2 genuine multi-entropy $\mathrm{GM}^{(\mathtt{q})}_2$ as a diagnostic of genuine $\mathtt{q}$-partite entanglement, we establish this behavior in $(2+1)$-dimensional gapped free-fermion lattices with correlation length $ξ$. For partitions with a single junction, $\mathrm{GM}^{(\mathtt{q})}_2$ exhibits a universal scaling crossover in $L/ξ$, growing for $L\llξ$ and saturating to a $ξ$-dependent constant for $L\ggξ$, up to $\mathcal{O}(e^{-L/ξ})$ corrections. In sharp contrast, for partitions without a junction, $\mathrm{GM}^{(\mathtt{q})}_2$ is exponentially suppressed in $L/ξ$ and drops below numerical resolution once $L\ggξ$. We observe the same pattern for $\mathtt{q}=3$ (tripartite) and $\mathtt{q}=4$ (quadripartite) cases, and further corroborate this localization by translating the junction at fixed system size. We also provide a geometric explanation of the junction law in holography. Altogether, these results show that in this gapped free-fermion setting genuine multipartite entanglement is localized within a correlation-length neighborhood of junctions.

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arXiv2026

Symmetry-resolved genuine multi-entropy: Haar random and graph states

We study the symmetry-resolved genuine multi-entropy, a measure that captures genuine multi-partite entanglement, in Haar random states and random graph states in the presence of a conserved quantity. For Haar random states, we derive explicit formulae for the genuine multi-entropy under a global $U(1)$ symmetry in the thermodynamic limit, and find that its dependence on subsystem sizes closely resembles that of fully Haar random states without a conserved charge. We also perform numerical analyses, focusing on spin systems for both Haar random and graph states. For random graph states, our numerical analyses reveal distinctive features of their multi-partite entanglement structure and we contrast them with the Haar random case.

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arXiv2025

Energy Conditions and Quantum Information

The concept of energy lies at the foundation of physical science. In general relativity and quantum field theory, the positivity and conservation of energy are encapsulated by the so-called energy-momentum tensor and the energy conditions. In recent efforts to unify fundamental physics with quantum information, the energy conditions have come to play a crucial role in establishing numerous theorems. In this article, we review the basics of energy conditions in general relativity and their applications in gravitational physics, quantum field theory, and the holographic principle. Through these applications, we explore the profound connection between the energy conditions and quantum information

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arXiv2025

Multipartite Markov Gaps and Entanglement Wedge Multiway Cuts

The Markov gap, defined as the difference between reflected entropy and mutual information, serves as a diagnostic for quantum recoverability and multipartite entanglement. In holographic settings, it admits a geometric interpretation as the deviation between entanglement wedge cross-sections and RT surfaces. Motivated by this holographic perspective, we propose a generalization of the Markov gap to multipartite systems by using a reflected multi-entropy. The resulting Multipartite Markov gap can capture geometric obstructions to bulk reconstruction. We investigate the properties of this quantity from both information-theoretic and holographic viewpoints, and examine its potential operational significance through candidate recovery maps. We further introduce the genuine reflected multi-entropy, which is designed to vanish for states containing only lower-partite entanglement. Together, these quantities offer complementary probes of recoverability and multipartite structure in holographic quantum systems.

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arXiv2025

More on genuine multi-entropy and holography

By generalizing the construction of genuine multi-entropy ${\rm GM}[\mathtt{q}]$ for genuine multi-partite entanglement proposed in the previous paper arXiv:2502.07995, we give a prescription on how to construct ${\rm GM}[\mathtt{q}]$ systematically for any $\mathtt{q}$. The crucial point is that our construction naturally fits to the partition number $p(\mathtt{a})$ of integer $\mathtt{a}$. For general $\mathtt{q}$, ${\rm GM}[\mathtt{q}]$ contains $N (\mathtt{q}) = p(\mathtt{q})-p(\mathtt{q}-1)-1$ number of free parameters. Furthermore, these give $N (\mathtt{q})+1$ number of new diagnostics for genuine $\mathtt{q}$-partite entanglement. Especially for $\mathtt{q}=4$ case, this reproduces not only the known diagnostics pointed out by arXiv:1406.2663, but also a new diagnostics for quadripartite entanglement. We also study these ${\rm GM}[\mathtt{q}]$ for $\mathtt{q} = 4, 5$ in holography and show that these are of the order of ${\cal{O}}\left(1/G_N \right)$ both analytically and numerically. Our results give evidence that genuine multipartite entanglement is ubiquitous in holography. We discuss the connection to quantum error correction and the role of genuine multipartite entanglement in bulk reconstruction.

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arXiv2025

Genuine multi-entropy and holography

Is bipartite entanglement sufficient for holography? Through the analysis of the Markov gap, it is known that the answer is no. In this paper, we give a new perspective on this issue from a different angle using a multi-entropy. We define a genuine $\mathtt{q}$-partite multi-entropy from a $\mathtt{q}$-partite multi-entropy by subtracting appropriate linear combinations of $\mathtt{\tilde{q}}$-partite multi-entropies for $\mathtt{\tilde{q}} < \mathtt{q}$, in such a way that the genuine $\mathtt{q}$-partite multi-entropy vanishes for all $\mathtt{\tilde{q}}$-partite entangled states. After studying several aspects, we apply it to black holes and holography. For the application to black holes, we see that such a genuine $\mathtt{q}$-partite multi-entropy is important only after the Page time. For the application to holography, we prove that non-bipartite multi-entropies are always positive and $\mathcal{O}\left({1/ G_N}\right)$, as long as boundary subregions are connected. This indicates that for holography, genuine multi-partite entanglement is not small and plays an important role.

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arXiv2025

Why many-partite entanglement is essential for holography

We argue that many-partite entanglement is ubiquitous in holography and holographic quantum error correction codes. We base our claim on genuine multi-entropy, a new measure for multi-partite entanglement. We also discuss a connection between the bulk IR reconstruction and many-partite entanglement on a large number of boundary subregions.

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arXiv2025

Black Hole Multi-Entropy Curves

We investigate the multi-partite entanglement structure of an evaporating black hole and its Hawking radiation by dividing the radiation into finer subsystems. We approximate an evaporating black hole and its radiation with a Haar-random state for this purpose. Using the multi-entropy of these configurations, we define a black hole multi-entropy curve, which describes how the multi-entropy changes during the black hole evaporation. This black hole multi-entropy curve is a natural generalization of the Page curve since the multi-entropy reduces to the entanglement entropy for the bi-partite case. The multi-entropy curve keeps increasing in the early time. It reaches the maximum value at the multi-entropy time, which is later than the Page time, and starts to decrease. However, it does not decrease to zero at the end of the black hole evaporation. This non-zero value of the multi-entropy represents the secret entanglement between Hawking particles.

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arXiv2025

A note on Centaur geometry -- probing IR de Sitter spacetime holography

We explore a Centaur geometry in JT gravity, which is an asymptotically AdS spacetime but in the IR admits a dS bubble with another AdS geometry in the deep IR. Thus, this geometry admits a holographic dual in the sense that it is asymptotically AdS. In an attempt to understand this geometry, we calculate the density of states of the putative boundary dual for such mixed geometries by evaluating the on-shell action. We compute the density of states analytically in the classical limit. The resultant density of states suggest that the degrees of freedom in the IR are reduced in such a putative boundary theory due to the IR modification corresponding to the dS bubble.

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arXiv2024

Dissipation in the $1/D$ expansion for planar matrix models

We consider the thermal behavior of a large number of matrix degrees of freedom in the planar limit. We work in $0+1$ dimensions, with $D$ matrices, and use $1/D$ as an expansion parameter. This can be thought of as a non-commutative large-$D$ vector model, with two independent quartic couplings for the two different orderings of the matrices. We compute a thermal two-point correlator to ${\cal O}(1/D)$ and find that the degeneracy present at large $D$ is lifted, with energy levels split by an amount $\sim 1/\sqrt{D}$. This implies a timescale for thermal dissipation $\sim \sqrt{D}$. At high temperatures dissipation is predominantly due to one of the two quartic couplings.

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arXiv2024

A note on the non-planar corrections for the Page curve in the PSSY model via the IOP matrix model correspondence

We develop a correspondence between the PSSY model and the IOP matrix model by comparing their Schwinger-Dyson equations, Feynman diagrams, and parameters. Applying this correspondence, we resum specific non-planar diagrams involving crossing in the PSSY model by using a non-planar analysis of a two-point function in the IOP matrix model. We also compare them with Page's formula on entanglement entropy and discuss the contributions of extra-handle-in-bulk diagrams.

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