arXiv subjects

Xin-Xiang Ju

Publications and source records attributed to Xin-Xiang Ju.

15 recordsLinked to original sources

arXiv2026

Long-range multipartite entanglement in holographic gapless systems

Gapless quantum systems support correlations over arbitrarily long distances, giving rise to power-law long-range entanglement. We investigate long-range entanglement at strong coupling for three-dimensional gapless systems using holography, asking whether multipartite entanglement can exhibit scale-growing behavior and become enhanced at large distances. We show that a broad class of multipartite entanglement quantities share the same leading large-distance scaling exponent determined by the IR geometry. To realize different scaling regimes, we consider hyperscaling-violating IR geometries. Depending on the parameters, long-distance multipartite entanglement can decay, become logarithmic, grow subextensively, or reach a volume law. We also analyze an anisotropic IR geometry $\mathrm{AdS}_{3}\times\mathbb{R}^{2}$, where long-range multipartite entanglement survives along one direction but becomes short-ranged in the transverse gapped directions. These results show that holographic gapless phases can support rich and enhanced long-range multipartite entanglement, providing a nonlocal characterization of the underlying IR physics.

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arXiv2026

Holographic multipartite entanglement dynamics in AdS$_3$-Vaidya

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.

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arXiv2026

The Holographic Multi-Entropy Cone

We generalize the holographic entropy cone (HEC) to the holographic multi-entropy cone (HMEC) by adjoining multi-entropy coordinates to the standard bipartition entropy coordinates. We show that holographic states, through their multi-entropy vectors, form a rational polyhedral cone in multi-entropy space, and multicontraction maps provide exact certificates for holographic multi-entropy inequalities (HMEIs). We determine all facets of the $n=3,4$ HMECs, where $n$ includes the purifier, and obtain seven fundamental HMEI orbits: two for $n=3$ and five for $n=4$. We further propose two structural conjectures: HEC facet inequalities are convex combinations of HMEC facet inequalities, and HMEC facets obey a balanced-but-not-too-balanced principle.

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arXiv2026

Sperner state and multipartite entanglement signals

We establish a systematic classification scheme for multipartite entanglement structures. We define Sperner states -- a broad class of states where apparent multipartite entanglement decomposes into fewer-partite entanglement among subsystems of each party. Each class of Sperner states is associated with one antichain hypergraph and each hypergraph encodes the maximal entanglement structure permissible under its constraints. We introduce a Multi-entanglement Measure Space (MEMS) where each Sperner class corresponds to a linear subspace defined by the vanishing of specific linear combinations of bipartite and multipartite measures. The nonvanishing of such combinations signals multipartite entanglement beyond the associated hypergraph, thereby distinguishing entanglement structures. We build a two way connection between each hypergraph entanglement structure and a distinct set of combinations, thereby quantifying the entanglement pattern and providing a unified basis for classifying all multipartite entanglement.

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arXiv2025

Entanglement wedge cross section triangle information and holographic entanglement of assistance

We identify a non-negative and upper-bounded entanglement signal in holography which is defined as a combination of entanglement wedge cross sections (EWCS) for a tripartite mixed state $ABE$: $\mathrm{EI}_Δ(A:B|E) = \mathrm{EWCS}(A:EB) + \mathrm{EWCS}(B:EA) - \mathrm{EWCS}(E:AB)$. This quantity is an analogue of conditional mutual information (CMI) and shares similar mathematical structures in both quantum information theory and holography. We show that CMI is upper bounded by a quantum information quantity, the entanglement of assistance, which quantifies the entanglement that can be generated between two parties $A$ and $B$, given assistance from a third party $E$. We prove that $\mathrm{EI}_Δ$ is also upper bounded by the entanglement of assistance in the canonical purification state. We analyze its upper bound by maximizing $\mathrm{EI}_Δ(A:B|E)$ over all configurations of the auxiliary subsystem $E$ in AdS$_3$/CFT$_2$. The maximized $\mathrm{EI}_Δ$ displays a rich phase structure governed by the cross ratio $X_{AB}$: it vanishes below a critical threshold and, beyond a second phase transition point, saturates the bound of entanglement of assistance. We comment on the interpretation of $\mathrm{EI}_Δ$ as characterizing the assisted bipartite quantum entanglement between $A$ and $B$ with the help of $E$.

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arXiv2025

Holographic multipartite entanglement structures in IR modified geometries

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.

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arXiv2025

Holographic geometry/real-space entanglement correspondence and metric reconstruction

In holography, the boundary entanglement structure is believed to be encoded in the bulk geometry. In this work, we investigate the precise correspondence between the boundary real-space entanglement and the bulk geometry. By the boundary real-space entanglement, we refer to the conditional mutual information (CMI) for two infinitesimal subsystems separated by a distance $l$, and the corresponding bulk geometry is at a radial position $z_*$, namely the turning point of the entanglement wedge for a boundary region with a length scale $l$. In a generic geometry described by a given coordinate system, $z_*$ can be determined locally by $l$, while the exact expression for $z_*(l)$ depends on the gauge choice, reflecting the inherent nonlocality of this seemingly local correspondence. We propose to specify the function $z_*(l)$ as the criterion for a gauge choice, and with the specified gauge function, we verify the exact correspondence between the boundary real-space entanglement and the bulk geometry. Inspired by this correspondence, we propose a new method of bulk metric reconstruction from boundary entanglement data, namely the CMI reconstruction. In this CMI proposal, with the gauge fixed a priori by specifying $z_*(l)$, the bulk metric can be reconstructed from the relation between the bulk geometry and the boundary CMI. The CMI reconstruction method establishes a connection between the differential entropy prescription and Bilson's general algorithm for metric reconstruction.

hep-th↗

arXiv2025

Upper bound of holographic entanglement entropy combinations

In this work, we develop a systematic formalism to evaluate the upper bound of a large family of holographic entanglement entropy combinations when fixing $n$ subsystems and fine-tuning one other subsystem. The upper bound configurations and values of these entropy combinations can be derived and classified. The upper bound of these entropy combinations reveals holographic $n+1$-partite entanglement that $n$ fixed subsystems participate in. In AdS$_3$/CFT$_2$, AdS$_4$/CFT$_3$, and even higher-dimensional holography, one can, in principle, find different formulas of upper bound values, reflecting the fundamental difference in entanglement structure in different dimensions.

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arXiv2025

Squashed Entanglement from Generalized Rindler Wedge

We investigate the bipartite and multipartite quantum entanglement structure in gravity and the dual holographic field theory based on the generalized Rindler wedge formalism. We deduce a separation theorem, which asserts that for subregions satisfying a certain geometric condition, the bipartite/multipartite squashed entanglement or the conditional entanglement of multipartite information vanishes, indicating that these subregions represent separable states with no quantum entanglement among them. We interpret this fact from the observer perspective in gravity and show how to probe the entanglement structure further in this framework by introducing a time cutoff in the gravitational spacetime. We also present the corresponding dual boundary field theory interpretation.

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arXiv2025

Modular Hamiltonian of holographic time band states

A holographic time band is a causal incomplete boundary spacetime subregion whose causal wedge is a causal complete bulk spacetime subregion. In an AdS$_3$ spacetime with a specifically modified IR geometry, its causal wedge coincides with its entanglement wedge, which suggests the existence of a local modular Hamiltonian for the holographic time band state. In this work, we construct the local modular Hamiltonian for holographic time bands using two independent methods: from the quantum information properties of the time band state and from the construction of consistent geometric modular flows. Both methods lead to the same unique result of the local modular Hamiltonian, reflecting the intrinsic property of the time band state. The entanglement first law has also been checked to hold for the simplest time band state. This is a substantial addition to the known holographic subsystems with a local modular Hamiltonian, beyond the few cases previously identified.

hep-th↗

arXiv2025

More on the upper bound of holographic n-partite information

We show that there exists a huge amount of multipartite entanglement in holography by studying the upper bound for holographic $n$-partite information $I_n$ that $n-1$ fixed boundary subregions participate. We develop methods to find the $n$-th region $E$ that makes $I_n$ reach the upper bound. Through the explicit evaluation, it is shown that $I_n$, an IR term without UV divergence, could diverge when the number of intervals or strips in region $E$ approaches infinity. At this upper bound configuration, we could argue that $I_n$ fully comes from the $n-$partite global quantum entanglement. Our results indicate: fewer-partite entanglement in holography emerges from more-partite entanglement; $n-1$ distant local subregions are highly $n$-partite entangling. Moreover, the relationship between the convexity of a boundary subregion and the multipartite entanglement it participates, and the difference between multipartite entanglement structure in different dimensions are revealed as well.

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arXiv2024

Generalized Rindler Wedge and Holographic Observer Concordance

Defining gravitational subsystems has long been challenging due to the lack of the conventional notion of locality in gravity. In this work, we define gravitational subsystems from the observable spacetime subregions of a set of well-defined accelerating observers. We study the most general horizons of accelerating observers and find that in a general spacetime, only spacelike surfaces satisfying a global condition could become horizons of well-defined accelerating observers, which we name the Rindler-convexity condition. The entanglement entropy associated with a Rindler-convex region is proportional to the area of the enclosing surface. The subregions defined from this observer perspective is named the generalized Rindler wedge. This provides a physical origin for defining gravitational subsystems associated with one type of Type III von Neumann subalgebra. We propose the holographic interpretation of generalized Rindler wedges and provide evidence from the observer correspondence, the subregion subalgebra duality, and the equality of the entanglement entropy, respectively. We introduce time/space cutoffs in the bulk to substantiate this proposition, generalize it, and establish a holographic observer concordance framework, which asserts that the partitioning of degrees of freedom through observation is holographically concordant.

hep-th↗

arXiv2024

Holographic multipartite entanglement from the upper bound of $n$-partite information

To analyze the holographic multipartite entanglement structure, we study the upper bound for holographic $n$-partite information $(-1)^n I_n$ that $n-1$ fixed boundary subregions participate together with an arbitrary region $E$. In general cases, we could find regions $E$ that make $I_n$ approach the upper bound. For $n=3$, we show that the upper bound of $-I_3$ is given by a quantity that we name the entanglement of state-constrained purification $EoSP(A:B)$. For $n\geq4$, we find that the upper bound of $I_n$ is finite in holographic CFT$_{1+1}$ but has UV divergences in higher dimensions, which reveals a fundamental difference in the entanglement structure in different dimensions. When $(-1)^n I_n$ reaches the information-theoretical upper bound, we argue that ( I_n ) fully accounts for multipartite global entanglement in these upper bound critical points, in contrast to usual cases where $I_n$ is not a perfect measure for multipartite entanglement. We further show that these results suggest that fewer-partite entanglement fully emerges from more-partite entanglement, and any $n-1$ distant regions are fully $n$-partite entangling in higher dimensions.

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arXiv2024

Entanglement structures from modified IR geometry

We investigate a new proposal connecting the geometry at various radial scales in asymptotic AdS spacetime with entanglement structure at corresponding real-space length scales of the boundary theory. With this proposal, the bulk IR geometry encodes the long-scale entanglement structure of the dual quantum system. We consider two distinct types of IR geometries, namely the spherical case and the hyperbolic case, which are intimately related to the physics of differential entropy and brane-world holography separately. We explore the corresponding change in the dual long-scale entanglement structures, utilizing the tools of the Ryu-Takayanagi formula, conditional mutual information, and partial entanglement entropy. The results indicate that modifying the IR geometry leads to a redistribution of entanglement at scales longer than a critical length determined by the location of the IR region, with the two modified IR geometries corresponding to two opposite ways of redistribution. Furthermore, we establish the maximum amount of entanglement that can be modified, which is proportional to the area of the IR region.

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arXiv2023

Holographic n-partite Information in Hyperscaling Violating Geometry

The $n$-partite information (nI) is formulated as a measure of multi-partite entanglement. Field theory computation revealed that the sign of nI is indefinite for $n\geq 3$, while holographic studies conjectured a sign property that holographic nI is non-negative/non-positive for even/odd $n$, with tripartite information (TI, $n=3$) proved. We investigate the aspects of nI with holographic duality in hyperscaling violating geometry. We confirm the conjectured sign property for strips of equal length with equal separation distance, and disprove this conjecture for $n>3$ with general configurations. Therefore, nI in field theories and holography exhibits compatibility except for $n=3$. We also discuss other properties of holographic nI with analytic computation: the monotonicity, linearity, relation to hyperscaling violating parameters, temperature and UV cutoff effects, and the physical implications. It is doubtful that nI is an effective measure of entanglement considering the indefinite sign, non-monotonicity, and quasi-linearity of its holographic dual. In this respect, we propose constraints on the multi-partite entanglement measures.

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