Upper Bound on Diffusivity.

The linear growth of operators in local quantum systems leads to an effective light cone even if the system is nonrelativistic. We show that the consistency of diffusive transport with this light cone places an upper bound on the diffusivity: D≲v^{2}τ_{eq}. The operator growth velocity v defines the light cone, and τ_{eq} is the local equilibration time scale, beyond which the dynamics of conserved densities is diffusive.