Holographic scattering requires a connected entanglement wedge

TL;DR

This paper demonstrates that certain bulk scattering processes in AdS/CFT require a connected entanglement wedge, linking boundary mutual information to bulk connectivity and implications for nonlocal quantum computation.

Contribution

It establishes a rigorous connection between boundary mutual information and the necessity of a connected entanglement wedge for holographic scattering processes, with improved proofs and implications for quantum computation.

Findings

Boundary regions with scattering have O(1/G_N) mutual information.

Such regions must have a connected entanglement wedge.

Implications for nonlocal quantum computation protocols.

Abstract

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. We also provide a direct link to entanglement wedge reconstruction by showing that the bulk scattering region must lie inside the connected entanglement wedge. Our construction implies the existence of nonlocal quantum computation protocols that are exponentially more efficient than the optimal protocols currently known.