  The Lieb-Robinson theorem states that information propagates with a finite
velocity in quantum systems on a lattice with nearest-neighbor interactions.
What are the speed limits on information propagation in quantum systems with
power-law interactions, which decay as $1/r^\alpha$ at distance $r$? Here, we
present a definitive answer to this question for all exponents $\alpha>2d$ and
all spatial dimensions $d$. Schematically, information takes time at least
$r^{\min\{1, \alpha-2d\}}$ to propagate a distance~$r$. As recent state
transfer protocols saturate this bound, our work closes a decades-long hunt for
optimal Lieb-Robinson bounds on quantum information dynamics with power-law
interactions.
