Reinforcement learning finds explicit graph realizations for three of six previously unresolved extreme rays of the N=6 holographic entropy cone and supplies evidence that the other three lie outside it.
A new characterization of the holographic entropy cone
6 Pith papers cite this work. Polarity classification is still indexing.
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abstract
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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Under the exposed-region condition for HRT surface pairs, graph models reproduce covariant holographic entropies via a Conditional No-Short-Cut Theorem, proving equivalence to the static entropy cone.
Defines tripartite complexity and complexity gap for three-subsystem states and reports that the gap has definite sign across holographic CV, Fisher-Rao, and Krylov measures, suggesting it as a building block for complexity inequalities.
Generalizes the holographic signal inequality to mixed states, finds violations due to vanishing Markov gap in some geometries, restores it on canonical purification, and conjectures a new inequality.
Derives several new quantum bit thread prescriptions equivalent to quantum extremal surfaces for static holographic states and introduces entanglement distribution functions organized into the entropohedron convex polytope.
Timelike mutual information is positive and weak monotonicity holds for non-overlapping timelike subregions in AdS3-Vaidya holography, but the timelike strong subadditivity is violated for overlapping intervals while Araki-Lieb and subadditivity hold.
citing papers explorer
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Exploring the holographic entropy cone via reinforcement learning
Reinforcement learning finds explicit graph realizations for three of six previously unresolved extreme rays of the N=6 holographic entropy cone and supplies evidence that the other three lie outside it.
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Graph models for covariant holographic entropy I
Under the exposed-region condition for HRT surface pairs, graph models reproduce covariant holographic entropies via a Conditional No-Short-Cut Theorem, proving equivalence to the static entropy cone.
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Complexity Inequalities for Quantum Subsystems
Defines tripartite complexity and complexity gap for three-subsystem states and reports that the gap has definite sign across holographic CV, Fisher-Rao, and Krylov measures, suggesting it as a building block for complexity inequalities.
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On a mixed-state extension of the holographic signal inequality
Generalizes the holographic signal inequality to mixed states, finds violations due to vanishing Markov gap in some geometries, restores it on canonical purification, and conjectures a new inequality.
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Quantum Bit Threads and the Entropohedron
Derives several new quantum bit thread prescriptions equivalent to quantum extremal surfaces for static holographic states and introduces entanglement distribution functions organized into the entropohedron convex polytope.
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Entanglement inequalities for timelike intervals within dynamical holography
Timelike mutual information is positive and weak monotonicity holds for non-overlapping timelike subregions in AdS3-Vaidya holography, but the timelike strong subadditivity is violated for overlapping intervals while Araki-Lieb and subadditivity hold.