  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.
