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The Holographic Multi-Entropy Cone

  • Xin-Xiang Ju
  • Yang Zhao
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Abstract

We generalize the holographic entropy cone (HEC) to the holographic multi-entropy cone (HMEC) by adjoining multi-entropy coordinates to the standard bipartition entropy coordinates. We show that holographic states, through their multi-entropy vectors, form a rational polyhedral cone in multi-entropy space, and multicontraction maps provide exact certificates for holographic multi-entropy inequalities (HMEIs). We determine all facets of the n=3,4 HMECs, where n includes the purifier, and obtain seven fundamental HMEI orbits: two for n=3 and five for n=4. We further propose two structural conjectures: HEC facet inequalities are convex combinations of HMEC facet inequalities, and HMEC facets obey a balanced-but-not-too-balanced principle.

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Cite

BibTeXRIS
BibTeX
@misc{ju2026holographic,
  title = {{The Holographic Multi-Entropy Cone}},
  author = {Xin-Xiang Ju and Yang Zhao},
  howpublished = {arXiv},
  year = {2026},
  month = jul,
  doi = {10.48550/arxiv.2606.15173},
  eprint = {2606.15173},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.15173},
}
RIS
TY  - UNPB
TI  - The Holographic Multi-Entropy Cone
AU  - Xin-Xiang Ju
AU  - Yang Zhao
PY  - 2026
DA  - 2026/07/14
PB  - arXiv
DO  - 10.48550/arxiv.2606.15173
UR  - https://arxiv.org/abs/2606.15173
AB  - We generalize the holographic entropy cone (HEC) to the holographic multi-entropy cone (HMEC) by adjoining multi-entropy coordinates to the standard bipartition entropy coordinates. We show that holographic states, through their multi-entropy vectors, form a rational polyhedral cone in multi-entropy space, and multicontraction maps provide exact certificates for holographic multi-entropy inequalities (HMEIs). We determine all facets of the n=3,4 HMECs, where n includes the purifier, and obtain seven fundamental HMEI orbits: two for n=3 and five for n=4. We further propose two structural conjectures: HEC facet inequalities are convex combinations of HMEC facet inequalities, and HMEC facets obey a balanced-but-not-too-balanced principle.
ER  -