Towards a complete classification of holographic entropy inequalities

Abstract

We propose a deterministic method to find all holographic entropy inequalities that have corresponding contraction maps and argue the completeness of our method. We use a triality between holographic entropy inequalities, contraction maps and partial cubes. More specifically, the validity of a holographic entropy inequality is implied by the existence of a contraction map, which we prove to be equivalent to finding an isometric embedding of a contracted graph. Thus, by virtue of the argued completeness of the contraction map proof method, the problem of finding all holographic entropy inequalities is equivalent to the problem of finding all contraction maps, which we translate to a problem of finding all image graph partial cubes. We give an algorithmic solution to this problem and characterize the complexity of our method. We also demonstrate interesting by-products, most notably, a procedure to generate candidate quantum entropy inequalities.

v1 23 pages, 4 figures. v2 typos fixed. v3 Appendix B added, more explanations in the text

References in corpus (19)

• A holographic proof of the strong subadditivity of entanglement entropy
• A new multi-partite entanglement measure and its holographic dual
• Fun with replicas: tripartitions in tensor networks and gravity
• Covariant bit threads
• Towards classification of holographic multi-partite entanglement measures
• Superbalance of Holographic Entropy Inequalities
• The Quantum Entropy Cone of Hypergraphs
• On the foundations and extremal structure of the holographic entropy cone
• Holographic Entropy Inequalities and Multipartite Entanglement
• The Symmetrized Holographic Entropy Cone
• Holographic Cone of Average Entropies
• The holographic entropy cone from marginal independence
• Multi-entropy at low Renyi index in 2d CFTs
• Topological Link Models of Multipartite Entanglement
• Two infinite families of facets of the holographic entropy cone
• Properties of the contraction map for holographic entanglement entropy inequalities
• Improved proof-by-contraction method and relative homologous entropy inequalities
• A framework for generalizing toric inequalities for holographic entanglement entropy
• Beyond the Holographic Entropy Cone via Cycle Flows

Cited by in corpus (6)

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• Upper bound of holographic entanglement entropy combinations
• Exploring the holographic entropy cone via reinforcement learning
• Topological entanglement entropy meets holographic entropy inequalities