Two infinite families of facets of the holographic entropy cone

Abstract

We verify that the recently proven infinite families of holographic entropy inequalities are maximally tight, i.e. they are facets of the holographic entropy cone. The proof is technical but it offers some heuristic insight. On star graphs, both families of inequalities quantify how concentrated / spread information is with respect to a dihedral symmetry acting on subsystems. In addition, toric inequalities viewed in the K-basis show an interesting interplay between four-party and six-party perfect tensors.

arXiv comment18 pages plus appendices, 8 figures, 18 lemmas. v4: one minor but crucial typo fixed

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• Purely GHZ-like entanglement is forbidden in holography
• On the completeness of contraction map proof method for holographic entropy inequalities
• Exploring the holographic entropy cone via reinforcement learning