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arXiv:2502.07995 · Physical review. D/Physical review. D.

Genuine multientropy and holography

Norihiro Iizuka, Mitsuhiro Nishida

Published Jun 6, 2025• 12 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/714c-byxq

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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.
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.
While entanglement is a cornerstone of quantum theory and holography, quantum correlations arising from superposition, such as quantum discord, offer a broader perspective that has remained largely unexplored in holography. We construct gravity duals of quantum discord and classical correlation. In both holographic systems and Haar random states, discord exceeds entanglement, revealing an additional quantum correlation linked to the Markov gap and non-distillable entanglement, suggesting holographic states are intrinsically non-bipartite. In black hole setups, discord can increase despite decoherence and persists beyond the sudden death of distillable entanglement. Motivated by the holographic formula, we define reflected discord -- an optimization-free boundary quantity based on reflected entropy -- which remains effective even outside the holographic regime. We also propose several multipartite generalizations of correlation measures. It includes holography-inspired correlations based on multi-entropy, which are shown to be UV-finite and reduce to bipartite measures in the bipartite limit. These results provide new tools for quantifying quantum correlations beyond entanglement in strongly coupled many-body systems and offer a novel approach to multipartite correlation measures.
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​.
A bstract 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.
Abstract Complex quantum information tasks in a gravitational background require multipartite entanglement for effective processing. Therefore, it is necessary to investigate the properties of multipartite entanglement in a relativistic setting. In this paper, we study genuine N-partite entanglement of massless Dirac fields in the Schwarzschild-de Sitter (SdS) spacetime, characterized by the presence of a black hole event horizon (BEH) and a cosmological event horizon (CEH). We obtain the general analytical expression of genuine N-partite entanglement shared by n observers near BEH and m ( n+m=Nn+m=Nn+m=N n + m = N ) observers near CEH. It is shown that genuine N-partite entanglement monotonically decreases with the decrease of the mass of the black hole, suggesting that the Hawking effect of the black hole destroys quantum entanglement. It is interesting to note that genuine N-partite entanglement is a non-monotonic function of the cosmological constant, meaning that the Hawking effect of the expanding universe can enhance quantum entanglement. This result contrasts with multipartite entanglement in single-event horizon spacetime, offering a new perspective on the Hawking effect in multi-event horizon spacetime.
Abstract We study genuine N-partite entanglement of massless Dirac fields new a black hole event horizon (BEH) and a cosmological event horizon (CEH) in the Schwarzschild–de Sitter (SdS) spacetime, respectively. We obtain the general analytical expression of genuine N-partite entanglement shared by N observers, each located near the BEH and CEH, respectively. It is shown that genuine N-partite entanglement situated near the BEH can decrease to zero with the decrease of the mass of the black hole, suggesting that the Hawking effect of the black hole destroys quantum entanglement. Because the Hawking effect of the black hole located near the CEH is very weak, its impact on quantum entanglement is negligible. In addition, choosing appropriate initial parameters is beneficial to protecting quantum entanglement in multi-event horizon spacetime.