Hypergraph min-cuts from quantum entropies

The von Neumann entropy of pure quantum states and the min-cut function weighted hypergraphs are both symmetric submodular functions. In this article, we explain coincidence by proving that any hypergraph can be approximated (up to an overall rescaling) entropies known as stabilizer states. We do so constructing a novel ensemble random states, built from tensor networks, whose entanglement structure is determined given hypergraph. This implies min-cuts constrained inequalities, it follows recently defined cones contained in cones, which confirms conjecture made recent literature.