  We theoretically study the response of a many-body localized system to a
local quench from a quantum information perspective. We find that the local
quench triggers entanglement growth throughout the whole system, giving rise to
a logarithmic lightcone. This saturates the modified Lieb-Robinson bound for
quantum information propagation in many-body localized systems previously
conjectured based on the existence of local integrals of motion. In addition,
near the localization-delocalization transition, we find that the final states
after the local quench exhibit volume-law entanglement. We also show that the
local quench induces a deterministic orthogonality catastrophe for highly
excited eigenstates, where the typical wave-function overlap between the pre-
and post-quench eigenstates decays {\it exponentially} with the system size.
