Geometric Quantum States Beyond AdS/CFT

We characterize the quantum states dual to entanglement wedges in arbitrary spacetimes, in settings where the matter entropy can be neglected compared to the geometric entropy. In AdS/CFT, such states obey special entropy inequalities known as the holographic entropy cone. In particular, the mutual information of CFT subregions is monogamous (MMI). We extend this result to arbitrary spacetimes, using a recent proposal for the generalized entanglement wedge e(a) of a gravitating region a. Given independent input regions a, b, and c, we prove MMI: Area[e(a)]+Area[e(b)]+Area[e(c)]-Area[e(ab)]-Area[e(bc)]-Area[e(ca)]+Area[e(abc)] $\leq$ 0. We expect that the full holographic entropy cone can be extended to arbitrary spacetimes using similar methods.