  We investigate the propagation of local bipartite quantum correlations, along
with the tripartite mutual information to characterize the information
scrambling through dynamical evolution of spin chains. Starting from an initial
state with the first pair of spins in a Bell state, we study how quantum
correlations spread to other parts of the system, using different
representative spin Hamiltonians, viz. the Heisenberg Model, a spin-conserving
model, the transverse-field XY model, a non-conserving but integrable model,
and the kicked Harper model, a spin conserving but nonintegrable model. We show
that the local correlations spread consistently in the case of spin-conserving
dynamics in both integrable and nonintegrable cases, with a strictly
nonnegative tripartite mutual information. In contrast, in the case of
non-conserving dynamics, tripartite mutual information is negative and local
pair correlations do not propagate.
