Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2511.21870

Zoo of Correlation Inequalities in Holography and Beyond

Kyan Louisia, Takato Mori, Herbie Warner

hep-thquant-phSubmitted Nov 26, 2025• Announced Nov 28, 2025• 0 citations• Revised Feb 2, 2026 (v2)
v1 · Nov 26, 2025v2 · Feb 2, 2026
arXivHTMLPDF

Abstract

Information-theoretic inequalities often impose nontrivial constraints on holographic states. In this work, we study measurement-based classical and quantum correlations in holography, focusing on the proposed duals of classical correlation $J_W$, quantum discord $D_W$, and one-shot distillable entanglement $E_D$, defined in terms of the entanglement wedge cross section (EWCS). We develop a homological framework tailored to inequalities involving multiple EWCSs and Ryu-Takayanagi surfaces, and use it to prove a family of inequalities, including monotonicity and monogamy/polygamy-type relations, as well as one-way strong superadditivity. For strong superadditivity, we additionally confirm its two-way version using Haar random states. We also examine holography-inspired boundary duals in terms of the reflected entropy and provide proofs and counterexamples for their information-theoretic inequalities. Taken together, our results provide further evidence for the duality between the EWCS and its proposed boundary counterparts -- measurement-based correlations and one-shot distillable entanglement -- while also furnishing a unified, rigorous method for proving multi-EWCS inequalities.

Comments
67 pages, 19 figures (v1); 73 pages, 22 figures, correction of proofs, rearrangement of text moving larger proofs to appendices, typos are corrected, updated abstract (v2)

Related papers

Zoo of correlation inequalities in holography and beyond

Kyan Louisia, Takato Mori, Herbie Warner

A bstract Information-theoretic inequalities often impose nontrivial constraints on holographic states. In this work, we study measurement-based classical and quantum correlations in holography, focusing on the proposed duals of classical correlation J W , quantum discord D W , and one-shot distillable entanglement E D , defined in terms of the entanglement wedge cross section (EWCS). We develop a homological framework tailored to inequalities involving multiple EWCSs and Ryu-Takayanagi surfaces, and use it to prove a family of inequalities, including monotonicity and monogamy/polygamy-type relations, as well as one-way strong superadditivity. For strong superadditivity, we additionally confirm its two-way version using Haar random states. We also examine holography-inspired boundary duals in terms of the reflected entropy and provide proofs and counterexamples for their information-theoretic inequalities. Taken together, our results provide further evidence for the duality between the EWCS and its proposed boundary counterparts — measurement-based correlations and one-shot distillable entanglement — while also furnishing a unified, rigorous method for proving multi-EWCS inequalities.

Journal of High Energy Physics•Jun 25, 2026•0 citations

Quantum correlation beyond entanglement: Holographic discord and multipartite generalizations

Takato Mori

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.

arXiv:2506.02131•Jun 2, 2025•0 citations

Quantum and classical correlations inside the entanglement wedge

Koji Umemoto

We show that the entanglement wedge cross section (EWCS) can become larger than the quantum entanglement measures such as the entanglement of formation in the AdS/CFT correspondence. We then discuss a series of holographic duals to the optimized correlation measures, finding a novel geometrical measure of correlation, the entanglement wedge mutual information (EWMI), as the dual of the $Q$-correlation. We prove that the EWMI satisfies the properties of the $Q$-correlation as well as the strong superadditivity, and that it can become larger than the entanglement measures. These results imply that both of the EWCS and the EWMI capture more than quantum entanglement in the entanglement wedge, which enlightens a potential role of classical correlations in holography.

arXiv:1907.12555•Physical review. D/Physical review. D.•Dec 20, 2019•46 citations

Holographic mutual information is monogamous

Patrick M. Hayden, Matthew Headrick, Alexander Maloney

We identify a special information-theoretic property of quantum field theories with holographic duals: the mutual informations among arbitrary disjoint spatial regions $A$, $B$, $C$ obey the inequality $I(A\ensuremath{\mathbin:}B\ensuremath{\cup}C)\ensuremath{\ge}I(A\ensuremath{\mathbin:}B)+I(A\ensuremath{\mathbin:}C)$, provided entanglement entropies are given by the Ryu-Takayanagi formula. Inequalities of this type are known as monogamy relations and are characteristic of measures of quantum entanglement. This suggests that correlations in holographic theories arise primarily from entanglement rather than classical correlations. We also show that the Ryu-Takayanagi formula is consistent with all known general inequalities obeyed by the entanglement entropy, including an infinite set recently discovered by Cadney et al.; this constitutes strong evidence in favor of its validity.

arXiv:1107.2940•Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields•Feb 6, 2013•326 citations

Holographic inequalities and entanglement of purification

Ning Bao, Illan F. Halpern

A bstract We study the conjectured holographic duality between entanglement of purification and the entanglement wedge cross-section. We generalize both quantities and prove several information theoretic inequalities involving them. These include upper bounds on conditional mutual information and tripartite information, as well as a lower bound for tripartite information. These inequalities are proven both holographically and for general quantum states. In addition, we use the cyclic entropy inequalities to derive a new holographic inequality for the entanglement wedge cross-section, and provide numerical evidence that the corresponding inequality for the entanglement of purification may be true in general. Finally, we use intuition from bit threads to extend the conjecture to holographic duals of suboptimal purifications.

arXiv:1710.07643•Journal of High Energy Physics•Mar 1, 2018•80 citations

Does connected wedge imply distillable entanglement?

Takato Mori, Beni Yoshida

A bstract The Ryu-Takayanagi formula predicts that two boundary subsystems A and C can exhibit large mutual information I ( A : C ) even when they are spatially disconnected on the boundary and separated by a buffer subsystem B , as long as A and C have connected entanglement wedge in the bulk. However, whether the reduced state ρ AC contains distillable EPR pairs has remained a longstanding open problem. In this work, we resolve this problem by showing that: i) there is no LO-distillable entanglement at leading order in G N , suggesting the absence of bipartite entanglement in a holographic mixed state ρ AC , and ii) one-shot, one-way LOCC-distillable entanglement is given at leading order by locally accessible information J W ( A | C ), which is related to the entanglement wedge cross section E W involving the (third) purifying system B via J W ( A | C ) = S A − E W ( A : B ). Namely, we demonstrate that a connected entanglement wedge does not necessarily imply nonzero distillable entanglement in one-shot, one-way LOCC. We also show that entanglement of formation E F ( A : C ) is given by E W ( A : C ) at leading order in holography.

arXiv:2411.03426•Journal of High Energy Physics•Jan 19, 2026•2 citations
Information-theoretic inequalities often impose nontrivial constraints on holographic states. In this work, we study measurement-based classical and quantum correlations in holography, focusing on the proposed duals of classical correlation JWJ_WJW​, quantum discord DWD_WDW​, and one-shot distillable entanglement EDE_DED​, defined in terms of the entanglement wedge cross section (EWCS). We develop a homological framework tailored to inequalities involving multiple EWCSs and Ryu-Takayanagi surfaces, and use it to prove a family of inequalities, including monotonicity and monogamy/polygamy-type relations, as well as one-way strong superadditivity. For strong superadditivity, we additionally confirm its two-way version using Haar random states. We also examine holography-inspired boundary duals in terms of the reflected entropy and provide proofs and counterexamples for their information-theoretic inequalities. Taken together, our results provide further evidence for the duality between the EWCS and its proposed boundary counterparts -- measurement-based correlations and one-shot distillable entanglement -- while also furnishing a unified, rigorous method for proving multi-EWCS inequalities.
A bstract Information-theoretic inequalities often impose nontrivial constraints on holographic states. In this work, we study measurement-based classical and quantum correlations in holography, focusing on the proposed duals of classical correlation J W , quantum discord D W , and one-shot distillable entanglement E D , defined in terms of the entanglement wedge cross section (EWCS). We develop a homological framework tailored to inequalities involving multiple EWCSs and Ryu-Takayanagi surfaces, and use it to prove a family of inequalities, including monotonicity and monogamy/polygamy-type relations, as well as one-way strong superadditivity. For strong superadditivity, we additionally confirm its two-way version using Haar random states. We also examine holography-inspired boundary duals in terms of the reflected entropy and provide proofs and counterexamples for their information-theoretic inequalities. Taken together, our results provide further evidence for the duality between the EWCS and its proposed boundary counterparts — measurement-based correlations and one-shot distillable entanglement — while also furnishing a unified, rigorous method for proving multi-EWCS inequalities.
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.
We show that the entanglement wedge cross section (EWCS) can become larger than the quantum entanglement measures such as the entanglement of formation in the AdS/CFT correspondence. We then discuss a series of holographic duals to the optimized correlation measures, finding a novel geometrical measure of correlation, the entanglement wedge mutual information (EWMI), as the dual of the QQQ-correlation. We prove that the EWMI satisfies the properties of the QQQ-correlation as well as the strong superadditivity, and that it can become larger than the entanglement measures. These results imply that both of the EWCS and the EWMI capture more than quantum entanglement in the entanglement wedge, which enlightens a potential role of classical correlations in holography.
We identify a special information-theoretic property of quantum field theories with holographic duals: the mutual informations among arbitrary disjoint spatial regions AAA, BBB, CCC obey the inequality $I(A\ensuremath{\mathbin:}B\ensuremath{\cup}C)\ensuremath{\ge}I(A\ensuremath{\mathbin:}B)+I(A\ensuremath{\mathbin:}C)$, provided entanglement entropies are given by the Ryu-Takayanagi formula. Inequalities of this type are known as monogamy relations and are characteristic of measures of quantum entanglement. This suggests that correlations in holographic theories arise primarily from entanglement rather than classical correlations. We also show that the Ryu-Takayanagi formula is consistent with all known general inequalities obeyed by the entanglement entropy, including an infinite set recently discovered by Cadney et al.; this constitutes strong evidence in favor of its validity.
A bstract We study the conjectured holographic duality between entanglement of purification and the entanglement wedge cross-section. We generalize both quantities and prove several information theoretic inequalities involving them. These include upper bounds on conditional mutual information and tripartite information, as well as a lower bound for tripartite information. These inequalities are proven both holographically and for general quantum states. In addition, we use the cyclic entropy inequalities to derive a new holographic inequality for the entanglement wedge cross-section, and provide numerical evidence that the corresponding inequality for the entanglement of purification may be true in general. Finally, we use intuition from bit threads to extend the conjecture to holographic duals of suboptimal purifications.
A bstract The Ryu-Takayanagi formula predicts that two boundary subsystems A and C can exhibit large mutual information I ( A : C ) even when they are spatially disconnected on the boundary and separated by a buffer subsystem B , as long as A and C have connected entanglement wedge in the bulk. However, whether the reduced state ρ AC contains distillable EPR pairs has remained a longstanding open problem. In this work, we resolve this problem by showing that: i) there is no LO-distillable entanglement at leading order in G N , suggesting the absence of bipartite entanglement in a holographic mixed state ρ AC , and ii) one-shot, one-way LOCC-distillable entanglement is given at leading order by locally accessible information J W ( A | C ), which is related to the entanglement wedge cross section E W involving the (third) purifying system B via J W ( A | C ) = S A − E W ( A : B ). Namely, we demonstrate that a connected entanglement wedge does not necessarily imply nonzero distillable entanglement in one-shot, one-way LOCC. We also show that entanglement of formation E F ( A : C ) is given by E W ( A : C ) at leading order in holography.