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arXiv:2411.03426 · Journal of High Energy Physics

Does connected wedge imply distillable entanglement?

Takato Mori, Beni Yoshida

Published Jan 19, 2026• 2 citations
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Abstract

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.

DOI
10.1007/jhep01(2026)125

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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.
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.
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 We study correlations between geometric subfactors living on the Ryu-Takayanagi surface that bounds the entanglement wedge. Using the surface-state correspondence and the bit threads program, we are able to calculate mutual information and conditional mutual information between subfactors. This enables us to count the shared Bell pairs between subfactors, and we propose an entanglement distillation procedure over these subsystems via a SWAP gate protocol. We comment on extending to multipartite entanglement.
A bstract In AdS/CFT, there can exist local 2-to-2 bulk scattering processes even when local scattering is not possible on the boundary; these have previously been studied in con- nection with boundary correlation functions. We show that boundary regions associated with these scattering configurations must have O (1 /G N ) mutual information, and hence a connected entanglement wedge. One of us previously argued for this statement from the boundary theory using operational tools in quantum information theory. We improve that argument to make it robust to small errors and provide a proof in the bulk using focusing arguments in general relativity. We also provide a direct link to entanglement wedge reconstruction by showing that the bulk scattering region must lie inside the con- nected entanglement wedge. Our construction implies the existence of nonlocal quantum computation protocols that are exponentially more efficient than the optimal protocols currently known.
A bstract We argue that holographic CFT states require a large amount of tripartite entanglement, in contrast to the conjecture that their entanglement is mostly bipartite. Our evidence is that this mostly-bipartite conjecture is in sharp conflict with two well- supported conjectures about the entanglement wedge cross section surface EW . If EW is related to either the CFT’s reflected entropy or its entanglement of purification, then those quantities can differ from the mutual information at O(1GN). O\left(\frac{1}{G_N}\right). O(GN​1​). O 1 G N . We prove that this implies holographic CFT states must have O(1GN). O\left(\frac{1}{G_N}\right). O(GN​1​). O 1 G N . amounts of tripartite entanglement. This proof involves a new Fannes-type inequality for the reflected entropy, which itself has many interesting applications.
We explore the fine structure of the holographic entanglement entropy proposal (the Ryu-Takayanagi formula) in AdS3_33​/CFT2_{2}2​. With the guidance from the boundary and bulk modular flows we find a natural slicing of the entanglement wedge with the modular planes, which are co-dimension one bulk surfaces tangent to the modular flow everywhere. This gives an one-to-one correspondence between the points on the boundary interval A\mathcal{A}A and the points on the Ryu-Takayanagi (RT) surface EA\mathcal{E}_{\mathcal{A}}EA​. In the same sense an arbitrary subinterval A2\mathcal{A}_2A2​ of A\mathcal{A}A will correspond to a subinterval E2\mathcal{E}_2E2​ of EA\mathcal{E}_{\mathcal{A}}EA​. We propose that the length of E2\mathcal{E}_2E2​ captures the contribution from A2\mathcal{A}_2A2​ to the entanglement entropy SAS_{\mathcal{A}}SA​, and compare it with the mutual information between A2\mathcal{A}_2A2​ and the complement Ac\mathcal{A}^cAc.