A bstract 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.
To analyze the holographic multipartite entanglement structure, we study the upper bound for holographic
n-partite information
(−1)nIn that
n−1 fixed boundary subregions participate together with an arbitrary region
E. In general cases, we could find regions
E that make
In approach the upper bound. For
n=3, we show that the upper bound of
−I3 is given by a quantity that we name the entanglement of state-constrained purification
EoSP(A:B). For
n≥4, we find that the upper bound of
In 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)nIn 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
In 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.
A bstract 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.
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.
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.
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 multientropy. We define a genuine q -partite multientropy from a q -partite multientropy by subtracting appropriate linear combinations of q ˜ -partite multientropies for q ˜ < q , in such a way that the genuine q -partite multientropy vanishes for all 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 q -partite multientropy is important only after the Page time. For the application to holography, we prove that nonbipartite multientropies are always positive and O ( 1 / G N ) , as long as boundary subregions are connected. This indicates that for holography, genuine multipartite entanglement is not small and plays an important role.
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.