Algorithmic construction of SSA-compatible extreme rays of the subadditivity cone and the $\mathsf{N}=6$ solution

Abstract

We compute the set of all extreme rays of the 6-party subadditivity cone that are compatible with strong subadditivity. In total, we identify 208 new (genuine 6-party) orbits, 52 of which violate at least one known holographic entropy inequality. For the remaining 156 orbits, which do not violate any such inequalities, we construct holographic graph models for 150 of them. For the final 6 orbits, it remains an open question whether they are holographic. Consistent with the strong form of the conjecture in arXiv:2204.00075, 148 of these graph models are trees. However, 2 of the graphs contain a "bulk cycle", leaving open the question of whether equivalent models with tree topology exist, or if these extreme rays are counterexamples to the conjecture. The paper includes a detailed description of the algorithm used for the computation, which is presented in a general framework and can be applied to any situation involving a polyhedral cone defined by a set of linear inequalities and a partial order among them to find extreme rays corresponding to down-sets in this poset.

51 pages, 2 figures, 8 tables; v3: changes in the introduction, published version

References in corpus (21)

• Gauge Theory Correlators from Non-Critical String Theory
• Holographic Derivation of Entanglement Entropy from AdS/CFT
• A Covariant Holographic Entanglement Entropy Proposal
• Holographic Mutual Information is Monogamous
• The Holographic Entropy Cone
• The Holographic Entropy Cone for Five Regions
• Holographic entropy relations
• A new inequality for the von Neumann entropy
• The holographic entropy arrangement
• Infinitely many constrained inequalities for the von Neumann entropy
• Stabilizer information inequalities from phase space distributions
• The Quantum Entropy Cone of Hypergraphs
• A holographic inequality for $N=7$ regions
• Holographic Entropy Inequalities and Multipartite Entanglement
• The holographic entropy cone from marginal independence
• Hypergraph min-cuts from quantum entropies
• On the relation between the subadditivity cone and the quantum entropy cone
• Two infinite families of facets of the holographic entropy cone
• A gap between holographic and quantum mechanical extreme rays of the subadditivity cone
• Inner bounding the quantum entropy cone with subadditivity and subsystem coarse grainings
• Tip of the Quantum Entropy Cone

Cited by in corpus (1)

• Exploring the holographic entropy cone via reinforcement learning