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:2512.24490

Necessary and sufficient conditions for entropy vector realizability by holographic simple tree graph models

Veronika E. Hubeny, Massimiliano Rota

hep-thquant-phSubmitted Dec 30, 2025• Announced Jan 1, 2026• 0 citations
arXivHTMLPDF

Abstract

We prove that the ``chordality condition'', which was established in arXiv:2412.18018 as a necessary condition for an entropy vector to be realizable by a holographic simple tree graph model, is also sufficient. The proof is constructive, demonstrating that the algorithm introduced in arXiv:2512.18702 for constructing a simple tree graph model realization of a given entropy vector that satisfies this condition always succeeds. We emphasize that these results hold for an arbitrary number of parties, and, given that any entropy vector realizable by a holographic graph model can also be realized, at least approximately, by a stabilizer state, they highlight how techniques originally developed in holography can provide broad insights into entanglement and information theory more generally, and in particular, into the structure of the stabilizer and quantum entropy cones. Moreover, if the strong form of the conjecture from arXiv:2204.00075 holds, namely, if all holographic entropy vectors can be realized by (not necessarily simple) tree graph models, then the result of this work demonstrates that the essential data that encodes the structure of the holographic entropy cone for an arbitrary number of parties, is the set of ``chordal'' extreme rays of the subadditivity cone.

Comments
25 pages, 2 figures

Related papers

On the construction of graph models realizing given entropy vectors

Veronika E. Hubeny, Massimiliano Rota

We present an efficient algorithm for the construction of a holographic simple tree graph model that realizes a given entropy vector, subject to a specific ``chordality'' condition first introduced in arXiv:2412.18018. We further develop the toolkit of the correlation hypergraph, particularly in relation to coarse-graining and fine-graining of subsystems. We then use these techniques to take the first steps towards the generalization of this new algorithm to arbitrary (not necessarily simple) holographic tree graph models, and the ``detection'' of unrealizability of an entropy vector independently from the knowledge of holographic entropy inequalities.

hep-thCross-listedarXiv:2512.18702•Dec 23, 2025

The holographic entropy cone from marginal independence

Sergio Hernández-Cuenca, Veronika E. Hubeny, Massimiliano Rota

Abstract The holographic entropy cone characterizes the relations between entanglement entropies for a spatial partitioning of the boundary spacetime of a holographic CFT in any state describing a classical bulk geometry. We argue that the holographic entropy cone, for an arbitrary number of parties, can be reconstructed from more fundamental data determined solely by subadditivity of quantum entropy. We formulate certain conjectures about graph models of holographic entanglement, for which we provide strong evidence, and rigorously prove that they all imply that such a reconstruction is possible. Our conjectures (except only for the weakest) further imply that the necessary data is remarkably simple. In essence, all one needs to know to reconstruct the holographic entropy cone, is a certain subset of the extreme rays of this simpler “subadditivity cone”, namely those which can be realized in holography. This recasting of the bewildering entanglement structure of geometric states into primal building blocks paves the way to distilling the essence of holography for the emergence of a classical bulk spacetime.

arXiv:2204.00075•Journal of High Energy Physics•Sep 22, 2022•20 citations

Exploring the holographic entropy cone via reinforcement learning

Temple He, Jaeha Lee, Hirosi Ooguri

We develop a reinforcement learning algorithm to study the holographic entropy cone. Given a target entropy vector, our algorithm searches for a graph realization whose min-cut entropies match the target vector. If the target vector does not admit such a graph realization, it must lie outside the cone, in which case the algorithm finds a graph whose corresponding entropy vector most nearly approximates the target and allows us to probe the location of the facets. For the $\sf N=3$ cone, we confirm that our algorithm successfully rediscovers monogamy of mutual information beginning with a target vector outside the holographic entropy cone. We then apply the algorithm to the $\sf N=6$ cone, analyzing the 6 "mystery" extreme rays of the subadditivity cone from arXiv:2412.15364 that satisfy all known holographic entropy inequalities yet lacked graph realizations. We found realizations for 3 of them, proving they are genuine extreme rays of the holographic entropy cone, while providing evidence that the remaining 3 are not realizable, implying unknown holographic inequalities exist for $\sf N=6$.

hep-thCross-listedarXiv:2601.19979•Journal of High Energy Physics•Jan 29, 2026•0 citations

The quantum entropy cone of hypergraphs

Ning Bao, Newton Cheng, Sergio Hernández-Cuenca +1 more

In this work, we generalize the graph-theoretic techniques used for the holographic entropy cone to study hypergraphs and their analogously-defined entropy cone. This allows us to develop a framework to efficiently compute entropies and prove inequalities satisfied by hypergraphs. In doing so, we discover a class of quantum entropy vectors which reach beyond those of holographic states and obey constraints intimately related to the ones obeyed by stabilizer states and linear ranks. We show that, at least up to 4 parties, the hypergraph cone is identical to the stabilizer entropy cone, thus demonstrating that the hypergraph framework is broadly applicable to the study of entanglement entropy. We conjecture that this equality continues to hold for higher party numbers and report on partial progress on this direction. To physically motivate this conjectured equivalence, we also propose a plausible method inspired by tensor networks to construct a quantum state from a given hypergraph such that their entropy vectors match.

arXiv:2002.05317•SciPost Physics•Nov 10, 2020•35 citations

Correlation hypergraph: a new representation of a quantum marginal independence pattern

Veronika E. Hubeny, Massimiliano Rota

A bstract We continue the study of the quantum marginal independence problem, namely the question of which faces of the subadditivity cone are achievable by quantum states. We introduce a new representation of the patterns of marginal independence (PMIs, corresponding to faces of the subadditivity cone) based on certain correlation hypergraphs, and demonstrate that this representation provides a more efficient description of a PMI, and consequently of the set of PMIs which are compatible with strong subadditivity. We then show that these correlation hypergraphs generalize to arbitrary quantum systems the well known relation between positivity of mutual information and connectivity of entanglement wedges in holography, and further use this representation to derive new results about the combinatorial structure of collections of simultaneously decorrelated subsystems specifying SSA-compatible PMIs. In the context of holography, we apply these techniques to derive a necessary condition for the realizability of entropy vectors by simple tree graph models, which were conjectured in [1] to provide the building blocks of the holographic entropy cone. Since this necessary condition is formulated in terms of chordality of a certain graph, it can be tested efficiently.

arXiv:2412.18018•Journal of High Energy Physics•Sep 10, 2025•2 citations

Gauge/Gravity Duality 2021

Veronika E. Hubeny

<!--HTML-->This talk will explain recent puzzling revelations in the ongoing efforts to obtain a useful characterization of entanglement structure of geometric states in a holographic CFT, via the so-called holographic entropy cone (HEC). The relations between subsystem entanglement entropies which delimit this cone are known explicitly for only a rather coarse subdivision of the system (specified by N spatial regions, for up to N = 5). We argue that, subject to a certain graph theoretic conjecture, the task of finding the HEC for arbitrary N can be recast in terms of a much simpler combinatorial one which effectively reduces to the connectivity of entanglement wedges. More specifically, the N-party HEC can be reconstructed by solving the holographic marginal independence problem (HMIP) for a finer subdivision N′ ≥ N, which technically amounts to identifying which extreme rays of this subadditivity cone are realizable holographically. Curiously, despite the fact that subadditivity is a universal property which states that total correlation cannot be negative, the non-trivial facets of the HEC constructed therefrom nevertheless cannot be recast as correlation measures.

•Jan 1, 2021•0 citations
We prove that the chordality condition'', which was established in arXiv:2412.18018 as a necessary condition for an entropy vector to be realizable by a holographic simple tree graph model, is also sufficient. The proof is constructive, demonstrating that the algorithm introduced in arXiv:2512.18702 for constructing a simple tree graph model realization of a given entropy vector that satisfies this condition always succeeds. We emphasize that these results hold for an arbitrary number of parties, and, given that any entropy vector realizable by a holographic graph model can also be realized, at least approximately, by a stabilizer state, they highlight how techniques originally developed in holography can provide broad insights into entanglement and information theory more generally, and in particular, into the structure of the stabilizer and quantum entropy cones. Moreover, if the strong form of the conjecture from arXiv:2204.00075 holds, namely, if all holographic entropy vectors can be realized by (not necessarily simple) tree graph models, then the result of this work demonstrates that the essential data that encodes the structure of the holographic entropy cone for an arbitrary number of parties, is the set of chordal'' extreme rays of the subadditivity cone.
We present an efficient algorithm for the construction of a holographic simple tree graph model that realizes a given entropy vector, subject to a specific ``chordality'' condition first introduced in arXiv:2412.18018. We further develop the toolkit of the correlation hypergraph, particularly in relation to coarse-graining and fine-graining of subsystems. We then use these techniques to take the first steps towards the generalization of this new algorithm to arbitrary (not necessarily simple) holographic tree graph models, and the ``detection'' of unrealizability of an entropy vector independently from the knowledge of holographic entropy inequalities.
Abstract The holographic entropy cone characterizes the relations between entanglement entropies for a spatial partitioning of the boundary spacetime of a holographic CFT in any state describing a classical bulk geometry. We argue that the holographic entropy cone, for an arbitrary number of parties, can be reconstructed from more fundamental data determined solely by subadditivity of quantum entropy. We formulate certain conjectures about graph models of holographic entanglement, for which we provide strong evidence, and rigorously prove that they all imply that such a reconstruction is possible. Our conjectures (except only for the weakest) further imply that the necessary data is remarkably simple. In essence, all one needs to know to reconstruct the holographic entropy cone, is a certain subset of the extreme rays of this simpler “subadditivity cone”, namely those which can be realized in holography. This recasting of the bewildering entanglement structure of geometric states into primal building blocks paves the way to distilling the essence of holography for the emergence of a classical bulk spacetime.
We develop a reinforcement learning algorithm to study the holographic entropy cone. Given a target entropy vector, our algorithm searches for a graph realization whose min-cut entropies match the target vector. If the target vector does not admit such a graph realization, it must lie outside the cone, in which case the algorithm finds a graph whose corresponding entropy vector most nearly approximates the target and allows us to probe the location of the facets. For the N=3\sf N=3N=3 cone, we confirm that our algorithm successfully rediscovers monogamy of mutual information beginning with a target vector outside the holographic entropy cone. We then apply the algorithm to the N=6\sf N=6N=6 cone, analyzing the 6 "mystery" extreme rays of the subadditivity cone from arXiv:2412.15364 that satisfy all known holographic entropy inequalities yet lacked graph realizations. We found realizations for 3 of them, proving they are genuine extreme rays of the holographic entropy cone, while providing evidence that the remaining 3 are not realizable, implying unknown holographic inequalities exist for N=6\sf N=6N=6.
In this work, we generalize the graph-theoretic techniques used for the holographic entropy cone to study hypergraphs and their analogously-defined entropy cone. This allows us to develop a framework to efficiently compute entropies and prove inequalities satisfied by hypergraphs. In doing so, we discover a class of quantum entropy vectors which reach beyond those of holographic states and obey constraints intimately related to the ones obeyed by stabilizer states and linear ranks. We show that, at least up to 4 parties, the hypergraph cone is identical to the stabilizer entropy cone, thus demonstrating that the hypergraph framework is broadly applicable to the study of entanglement entropy. We conjecture that this equality continues to hold for higher party numbers and report on partial progress on this direction. To physically motivate this conjectured equivalence, we also propose a plausible method inspired by tensor networks to construct a quantum state from a given hypergraph such that their entropy vectors match.
A bstract We continue the study of the quantum marginal independence problem, namely the question of which faces of the subadditivity cone are achievable by quantum states. We introduce a new representation of the patterns of marginal independence (PMIs, corresponding to faces of the subadditivity cone) based on certain correlation hypergraphs, and demonstrate that this representation provides a more efficient description of a PMI, and consequently of the set of PMIs which are compatible with strong subadditivity. We then show that these correlation hypergraphs generalize to arbitrary quantum systems the well known relation between positivity of mutual information and connectivity of entanglement wedges in holography, and further use this representation to derive new results about the combinatorial structure of collections of simultaneously decorrelated subsystems specifying SSA-compatible PMIs. In the context of holography, we apply these techniques to derive a necessary condition for the realizability of entropy vectors by simple tree graph models, which were conjectured in [1] to provide the building blocks of the holographic entropy cone. Since this necessary condition is formulated in terms of chordality of a certain graph, it can be tested efficiently.
<!--HTML-->This talk will explain recent puzzling revelations in the ongoing efforts to obtain a useful characterization of entanglement structure of geometric states in a holographic CFT, via the so-called holographic entropy cone (HEC). The relations between subsystem entanglement entropies which delimit this cone are known explicitly for only a rather coarse subdivision of the system (specified by N spatial regions, for up to N = 5). We argue that, subject to a certain graph theoretic conjecture, the task of finding the HEC for arbitrary N can be recast in terms of a much simpler combinatorial one which effectively reduces to the connectivity of entanglement wedges. More specifically, the N-party HEC can be reconstructed by solving the holographic marginal independence problem (HMIP) for a finer subdivision N′ ≥ N, which technically amounts to identifying which extreme rays of this subadditivity cone are realizable holographically. Curiously, despite the fact that subadditivity is a universal property which states that total correlation cannot be negative, the non-trivial facets of the HEC constructed therefrom nevertheless cannot be recast as correlation measures.