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On the foundations and extremal structure of the holographic entropy cone

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arxiv 2102.07535 v4 pith:5ZUPNNLR submitted 2021-02-15 math.CO quant-ph

David Avis , Sergio Hernández-Cuenca This is my paper · ORCID
classification math.COquant-ph
keywords coneentropyresultscompletedescriptiondevelopgraph-theoreticgraphs
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abstract

The holographic entropy cone (HEC) is a polyhedral cone first introduced in the study of a class of quantum entropy inequalities. It admits a graph-theoretic description in terms of minimum cuts in weighted graphs, a characterization which naturally generalizes the cut function for complete graphs. Unfortunately, no complete facet or extreme-ray representation of the HEC is known. In this work, starting from a purely graph-theoretic perspective, we develop a theoretical and computational foundation for the HEC. The paper is self-contained, giving new proofs of known results and proving several new results as well. These are also used to develop two systematic approaches for finding the facets and extreme rays of the HEC, which we illustrate by recomputing the HEC on $5$ terminals and improving its graph description. We also report on some partial results for $6$ terminals. Some interesting open problems are stated throughout.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. The Holographic Multi-Entropy Cone

    hep-th 2026-06 accept novelty 7.0 of 10

    Holographic multi-entropy vectors form a rational polyhedral cone; its n=3,4 facets yield seven fundamental multi-entropy inequality orbits, with ordinary HEC facets arising as convex combinations of HMEC facets.

  2. On the construction of graph models realizing given entropy vectors

    hep-th 2025-12 conditional novelty 7.0 of 10

    An efficient algorithm constructs candidate simple tree graph models for entropy vectors that pass a chordality test, but its correctness remains conjectural.

  3. More on the upper bound of holographic n-partite information

    hep-th 2024-11 conditional novelty 7.0 of 10

    The upper bound of holographic conditional mutual information equals twice the entanglement of state-constrained purification and diverges in the many-interval limit, revealing abundant multipartite entanglement.

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