  The Lieb-Robinson bound states that local Hamiltonian evolution in
nonrelativistic quantum mechanical theories gives rise to the notion of an
effective light-cone with exponentially decaying tails. We discuss several
consequences of this result in the context of quantum information theory.
First, we show that the information that leaks out to space-like separated
regions is negligable, and that there is a finite speed at which correlations
and entanglement can be distributed. Second, we discuss how these ideas can be
used to prove lower bounds on the time it takes to convert states without
topological quantum order to states with that property. Finally, we show that
the rate at which entropy can be created in a block of spins scales like the
boundary of that block.
