Holographic scattering requires a connected entanglement wedge

Understand

In AdS/CFT, there can exist local 2-to-2 bulk scattering processes even when local scattering is not possible on the boundary; these have previously been studied in connection with boundary correlation functions.

• We show that boundary regions associated with these scattering configurations must have $O(1/G_N)$ mutual information, and hence a connected entanglement wedge.
• One of us previously argued for this statement from the boundary theory using operational tools in quantum information theory.
• We improve that argument to make it robust to small errors and provide a proof in the bulk using focusing arguments in general relativity.