8 problems

Hypergraph generalization conjecture. Every entropy vector representable by a hypergraph can be represented using the cycle-flow prescription on a nesting balanced network.

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 vec…

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 QLR cone be the cone defined by the quantu…

Let $G_K$ be a hypergraph defining a $K$-party state construction, and let $\Ket{G_K}$ denote the resulting $K$-party quantum state. The construction uses AME tensors at bulk verti…

Let $\Sigma$ be a network with $n\geq2$ boundary vertices. An extremal-ray realization is a subnetwork whose entropy vector realizes an extremal ray of the $n$-boundary-region holo…

Let $\Sigma$ be a network with four boundary vertices $A_1,\ldots,A_4$, and let $I(A_i:A_j)$ denote the mutual information between $A_i$ and $A_j$ on $\Sigma$. Let…

Let $|\psi\rangle_{A_1\dots A_n}$ be a pure state on $n$ parties. An extremal ray of the $n$-party holographic entropy cone is an extremal ray in that cone, represented by a state.…

Let $n$ denote the number of regions, and consider the cone of entropy vectors arising from von Neumann entropy for $n$ regions. Non-polyhedrality conjecture. The cone is not polyh…