Hypergraph min-cuts from quantum entropies

Abstract

The min-cut function of weighted hypergraphs and the von Neumann entropy of pure quantum states are both symmetric submodular functions. In this note, we explain this coincidence by proving that the min-cut function of any weighted hypergraph can be approximated (up to an overall rescaling) by the entropies of quantum states known as stabilizer states. This implies that the min-cuts of hypergraphs are constrained by quantum entropy inequalities, and it shows that the recently defined hypergraph cones are contained in the quantum stabilizer entropy cones, as has been conjectured in the recent literature.

arXiv comment5 pages

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• Random tensor networks with nontrivial links
• The Symmetrized Holographic Entropy Cone
• The holographic entropy cone from marginal independence
• Topological Link Models of Multipartite Entanglement
• On the relation between the subadditivity cone and the quantum entropy cone
• Testing holographic entropy inequalities in 2+1 dimensions
• Properties of the contraction map for holographic entanglement entropy inequalities
• 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
• Improved proof-by-contraction method and relative homologous entropy inequalities
• The resource theory of tensor networks
• Beyond the Holographic Entropy Cone via Cycle Flows
• Algorithmic construction of SSA-compatible extreme rays of the subadditivity cone and the $\mathsf{N}=6$ solution
• Discrete Bulk Reconstruction
• Exploring the holographic entropy cone via reinforcement learning