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Two infinite families of facets of the holographic entropy cone
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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.
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Cited by 3 Pith papers
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Algorithmic construction of SSA-compatible extreme rays of the subadditivity cone and the ${\sf N}=6$ solution
Complete classification of SSA-compatible extreme rays of the six-party subadditivity cone, with 150 holographic graph realizations and 52 confirmed non-holographic orbits.
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The Holographic Multi-Entropy Cone
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.
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On the construction of graph models realizing given entropy vectors
An efficient algorithm constructs candidate simple tree graph models for entropy vectors that pass a chordality test, but its correctness remains conjectural.
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