Holographic cone of average entropies

Abstract

AbstractThe holographic entropy cone identifies entanglement entropies of field theory regions, which are consistent with representing semiclassical spacetimes under gauge/gravity (holographic) duality. It is currently known up to five regions. Here we point out that average entropies of p-partite subsystems can be similarly analyzed for arbitrarily many regions. We conjecture that the holographic cone of average entropies is simplicial and specify all its bounding inequalities and extreme rays, which combine features of perfect tensor and bipartite entanglement. Heuristically, the conjecture posits that bipartite entanglement achieves the most efficient purification consistent with a holographic spacetime interpretation. We also explain that the extreme forms of entanglement allowed by our conjecture are realized by evaporating black holes.