Propagation of information in long-range quantum systems

We present bounds on the minimal time for quantum messaging, propagation/creation of correlations, and control of states for general, long-range, lattice quantum many-body bosonic systems. The proofs are based on a maximal velocity bound and the light-cone approximation of dynamics, which provide different expressions of the fact that the many-body evolution stays, up to small leaking probability tails, within a light cone of the support of the initial conditions and imply, in particular, Lieb-Robinson-type bounds on commutators of evolving observables.