The Holographic Multi-Entropy Cone
arXiv:2606.15173
The paper extends the holographic entropy cone by adding multi‑entropy coordinates, showing that holographic states form a rational polyhedral cone in this enlarged space and determining all facet inequalities for three‑ and four‑party cases, while proposing structural conjectures about these facets.
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 HMECs, where includes the purifier, and obtain seven fundamental HMEI orbits: two for and five for . 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.
v2: 29 pages, 5 figures, references added