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/rα at distance r? Here, we present a definitive answer to this question for all exponents α>2d and all spatial dimensions d. Schematically, information takes time at least rmin{1,α−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.

1 aTran, Minh, C.1 aGuo, Andrew, Y.1 aBaldwin, Christopher, L.1 aEhrenberg, Adam1 aGorshkov, Alexey, V.1 aLucas, Andrew uhttps://arxiv.org/abs/2103.15828