The hypergraph–stabilizer cone equality conjecture

For each $n$, let the $n$-party hypergraph cone be the cone of entropy vectors obtained from $n$-party hypergraphs, and let the $n$-party stabilizer cone be the cone of entropy vectors obtained from $n$-party stabilizer states. Hypergraph–stabilizer cone conjecture. The $n$-party hypergraph and stabilizer cones coincide for all $n$. The equality is established at four parties because the hypergraph, stabilizer, and QLR cones coincide there, while for larger numbers of parties the stabilizer cone is not fully characterized and the conjecture remains open.