arXiv subjects

Veronika E. Hubeny

Publications and source records attributed to Veronika E. Hubeny.

At least 19 recordsLinked to original sources

arXiv2026

Tripartite Form Universality in Holographic Entropy Inequalities

To elucidate the meaning of holographic entropy inequalities (beyond subadditivity) which characterize the entanglement structure of geometric states in holography, arXiv:2309.06296 proposed the "tripartite form" for these inequalities, consisting of tripartite information and conditional tripartite information terms with unit coefficients. While this provides a compact and useful packaging of the inequalities, it is not a priori guaranteed that all inequalities can be recast in this form. Here we conjecture that they can, and present substantial evidence, by proving that the two known infinite families of holographic entropy inequalities found in arXiv:2309.15145 can indeed be written in the tripartite form. This is significant because such recasting is particularly nontrivial for these families. Apart from providing the explicit tripartite form expressions for every member of these two infinite families, we detail how we arrived at them, in the process deriving several useful identities which may serve as stepping stones to formulate further repackaging of the corresponding information quantities. We also illustrate the power of the tripartite form by proving a number of structural properties satisfied by any holographic entropy inequality.

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arXiv2026

On the construction of graph models realizing given entropy vectors

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.

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arXiv2026

A new characterization of the holographic entropy cone

Entanglement entropies computed using the holographic Ryu-Takayanagi formula are known to obey an infinite set of linear inequalities, which define the so-called RT entropy cone. The general structure of this cone, or equivalently the set of all valid inequalities, is unknown. It is also unknown whether those same inequalities are also obeyed by entropies computed using the covariant Hubeny-Rangamani-Takayanagi formula, although significant evidence has accumulated that they are. Using Markov states, we develop a test of this conjecture in a heretofore unexplored regime. The test reduces to checking that a given inequality obeys a certain majorization property, which is easy to evaluate. We find that the RT inequalities pass this test and, surprisingly, only RT inequalities do so. Our results not only provide strong new evidence that the HRT and RT cones coincide, but also offer a completely new characterization of that cone.

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arXiv2026

Combinatorial properties of holographic entropy inequalities

A holographic entropy inequality (HEI) is a linear inequality obeyed by Ryu-Takayanagi holographic entanglement entropies, or equivalently by the minimum cut function on weighted graphs. We establish a new combinatorial framework for studying HEIs, and use it to prove several properties they share, including two majorization-related properties as well as a necessary and sufficient condition for an inequality to be an HEI. We thereby resolve all the conjectures presented in [arXiv:2508.21823], proving two of them and disproving the other two. In particular, we show that the null reduction of any superbalanced HEI passes the majorization test defined in [arXiv:2508.21823], thereby providing strong new evidence that all HEIs are obeyed in time-dependent holographic states.

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arXiv2025

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

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.

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arXiv2025

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

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 arXiv:2204.00075 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.

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arXiv2025

Algorithmic construction of SSA-compatible extreme rays of the subadditivity cone and the ${\sf N}=6$ solution

We compute the set of all extreme rays of the 6-party subadditivity cone that are compatible with strong subadditivity. In total, we identify 208 new (genuine 6-party) orbits, 52 of which violate at least one known holographic entropy inequality. For the remaining 156 orbits, which do not violate any such inequalities, we construct holographic graph models for 150 of them. For the final 6 orbits, it remains an open question whether they are holographic. Consistent with the strong form of the conjecture in arXiv:2204.00075, 148 of these graph models are trees. However, 2 of the graphs contain a "bulk cycle", leaving open the question of whether equivalent models with tree topology exist, or if these extreme rays are counterexamples to the conjecture. The paper includes a detailed description of the algorithm used for the computation, which is presented in a general framework and can be applied to any situation involving a polyhedral cone defined by a set of linear inequalities and a partial order among them to find extreme rays corresponding to down-sets in this poset.

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arXiv2025

Testing holographic entropy inequalities in 2+1 dimensions

We address the question of whether holographic entropy inequalities obeyed in static states (by the RT formula) are always obeyed in time-dependent states (by the HRT formula), focusing on the case where the bulk spacetime is 2+1 dimensional. An affirmative answer to this question was previously claimed by Czech-Dong. We point out an error in their proof when the bulk is multiply connected. We nonetheless find strong support, of two kinds, for an affirmative answer in that case. We extend the Czech-Dong proof for simply-connected spacetimes to spacetimes with $π_1=\mathbb{Z}$ (i.e. 2-boundary, genus-0 wormholes). Specializing to vacuum solutions, we also numerically test thousands of distinct inequalities (including all known RT inequalities for up to 6 regions) on millions of randomly chosen configurations of regions and bulk spacetimes, including three different multiply-connected topologies; we find no counterexamples. In an appendix, we prove some (dimension-independent) facts about degenerate HRT surfaces and symmetry breaking.

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arXiv2025

Minimax surfaces and the holographic entropy cone

We study and prove properties of the minimax formulation of the HRT holographic entanglement entropy formula, which involves finding the maximal-area surface on a timelike hypersurface, or time-sheet, and then minimizing over the choice of time-sheet. In this formulation, the homology condition is imposed at the level of the spacetime: the homology regions are spacetime volumes rather spatial regions. We show in particular that the smallest minimax homology region is the entanglement wedge. The minimax prescription suggests a way to construct a graph model for time-dependent states, a weighted graph on which min cuts compute HRT entropies. The existence of a graph model would imply that HRT entropies obey the same inequalities as RT entropies, in other words that the RT and HRT entropy cones coincide. Our construction of a graph model relies on the time-sheets obeying a certain ``cooperating'' property, which we show holds in some examples and for which we give a partial proof; however, we also find scenarios where it may fail.

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arXiv2024

Holographic Entropy Inequalities and Multipartite Entanglement

We study holographic entropy inequalities and their structural properties by making use of a judicious grouping of terms into certain multipartite information quantities. This allows us to recast cumbersome entropic expressions into much simpler ones which share interestingly rigid structures. By performing a systematic search over some of these structures, we are able to discover more than 300 novel entropy inequalities for six parties, thereby demonstrating that these recastings provide a fruitful generating technique for uncovering new holographic entropy inequalities. In attempting to interpret the corresponding sign-definite quantities as correlation measures, we also obtain a no-go result: the superbalance property of holographic entropy inequalities turns out to preclude them from being monotonic under partial tracing. In the process, we also comment on the geometrical significance of multipartite information quantities and present various structural relations amongst them.

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arXiv2024

Inner bounding the quantum entropy cone with subadditivity and subsystem coarse grainings

We show via explicit construction that all the extreme rays of both the three-party quantum entropy cone and the four-party stabilizer entropy cone can be obtained from subsystem coarse grainings of specific higher-party quantum states, namely extreme states characterized by saturating a (non-trivial) maximal set of instances of subadditivity. This suggests that the study of the ``subadditivity cone'', and the set of its extreme rays realizable in quantum mechanics, provides a powerful tool for deriving inner bounds for the quantum and stabilizer entropy cones, as well as constraints on new inequalities for the von Neumann entropy.

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arXiv2023

On the relation between the subadditivity cone and the quantum entropy cone

Given a multipartite quantum system, what are the possible ways to impose mutual independence among some subsystems, and the presence of correlations among others, such that there exists a quantum state which satisfies these demands? This question and the related notion of a \textit{pattern of marginal independence} (PMI) were introduced in arXiv:1912.01041, and then argued in arXiv:2204.00075 to be central in the derivation of the holographic entropy cone. Here we continue the general information theoretic analysis of the PMIs allowed by \textit{strong subadditivity} (SSA) initiated in arXiv:1912.01041. We show how the computation of these PMIs simplifies when SSA is replaced by a weaker constraint, dubbed \textit{Klein's condition} (KC), which follows from the necessary condition for the saturation of subadditivity (SA). Formulating KC in the language of partially ordered sets, we show that the set of PMIs compatible with KC forms a lattice, and we investigate several of its structural properties. One of our main results is the identification of a specific lower dimensional face of the SA cone that contains on its boundary all the extreme rays (beyond Bell pairs) that can possibly be realized by quantum states. We verify that for four or more parties, KC is strictly weaker than SSA, but nonetheless the PMIs compatible with SSA can easily be derived from the KC-compatible ones. For the special case of 1-dimensional PMIs, we conjecture that KC and SSA are in fact equivalent. To make the presentation self-contained, we review the key ingredients from lattice theory as needed.

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arXiv2023

A gap between holographic and quantum mechanical extreme rays of the subadditivity cone

We show via explicit construction that for six or more parties, there exist extreme rays of the subadditivity cone that can be realized by quantum states, but not by holographic states. This is a counterexample to a conjecture first formulated in arXiv:2204.00075, and implies the existence of deep holographic constraints that restrict the allowed patterns of independence among various subsystems beyond the universal quantum mechanical restrictions.

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arXiv2022

Report of the Snowmass 2021 Theory Frontier Topical Group on Quantum Information Science

We summarize current and future applications of quantum information science to theoretical high energy physics. Three main themes are identified and discussed; quantum simulation, quantum sensors and formal aspects of the connection between quantum information and gravity. Within these themes, there are important research questions and opportunities to address them in the years and decades ahead. Efforts in developing a diverse quantum workforce are also discussed. This work summarizes the subtopical area Quantum Information for High Energy Physics TF10 which forms part of the Theory Frontier report for the Snowmass 2021 planning process.

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arXiv2022

Covariant bit threads

We derive several new reformulations of the Hubeny-Rangamani-Takayanagi covariant holographic entanglement entropy formula. These include: (1) a minimax formula, which involves finding a maximal-area achronal surface on a timelike hypersurface homologous to D(A) (the boundary causal domain of the region A whose entropy we are calculating) and minimizing over the hypersurface; (2) a max V-flow formula, in which we maximize the flux through D(A) of a divergenceless bulk 1-form V subject to an upper bound on its norm that is non-local in time; and (3) a min U-flow formula, in which we minimize the flux over a bulk Cauchy slice of a divergenceless timelike 1-form U subject to a lower bound on its norm that is non-local in space. The two flow formulas define convex programs and are related to each other by Lagrange duality. For each program, the optimal configurations dynamically find the HRT surface and the entanglement wedges of A and its complement. The V-flow formula is the covariant version of the Freedman-Headrick bit thread reformulation of the Ryu-Takayanagi formula. We also introduce a measure-theoretic concept of a "thread distribution", and explain how Riemannian flows, V-flows, and U-flows can be expressed in terms of thread distributions.

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arXiv2022

The holographic entropy cone from marginal independence

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.

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arXiv2020

Superbalance of Holographic Entropy Inequalities

The domain of allowed von Neumann entropies of a holographic field theory carves out a polyhedral cone -- the holographic entropy cone -- in entropy space. Such polyhedral cones are characterized by their extreme rays. For an arbitrary number of parties, it is known that the so-called perfect tensors are extreme rays. In this work, we constrain the form of the remaining extreme rays by showing that they correspond to geometries with vanishing mutual information between any two parties, ensuring the absence of Bell pair type entanglement between them. This is tantamount to proving that besides subadditivity, all non-redundant holographic entropy inequalities are superbalanced, i.e. not only do UV divergences cancel in the inequality itself (assuming smooth entangling surfaces), but also in the purification thereof.

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arXiv2020

Large-$d$ phase transitions in holographic mutual information

In the AdS/CFT correspondence, the entanglement entropy of subregions in the boundary CFT is conjectured to be dual to the area of a bulk extremal surface at leading order in $G_N$ in the holographic limit. Under this dictionary, distantly separated regions in the CFT vacuum state have zero mutual information at leading order, and only attain nonzero mutual information at this order when they lie close enough to develop significant classical and quantum correlations. Previously, the separation at which this phase transition occurs for equal-size ball-shaped regions centered at antipodal points on the boundary was known analytically only in $3$ spacetime dimensions. Inspired by recent explorations of general relativity at large-$d$, we compute the separation at which the phase transition occurs analytically in the limit of infinitely many spacetime dimensions, and find that distant regions cannot develop large correlations without collectively occupying the entire volume of the boundary theory. We interpret this result as illustrating the spatial decoupling of holographic correlations in the large-$d$ limit, and provide intuition for this phenomenon using results from quantum information literature. We also compute the phase transition separation numerically for a range of bulk spacetime dimensions from $4$ to $21$, where analytic results are intractable but numerical results provide insight into the dimension-dependence of holographic correlations. For bulk dimensions above $5$, our exact numerical results are well approximated analytically by working to next-to-leading order in the large-$d$ expansion.

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