  In many-body localized systems, propagation of information forms a light cone
that grows logarithmically with time. However, local changes in energy or other
conserved quantities typically spread only within a finite distance. Is it
possible to detect the logarithmic light cone generated by a local perturbation
from the response of a local operator at a later time? We numerically calculate
various correlators in the random-field Heisenberg chain. While the equilibrium
retarded correlator $A(t=0)B(t>0)$ is not sensitive to the unbounded
information propagation, the out-of-time-ordered correlator
$A(t=0)B(t>0)A(t=0)B(t>0)$ can detect the logarithmic light cone. We relate
out-of-time-ordered correlators to the Lieb-Robinson bound in many-body
localized systems, and show how to detect the logarithmic light cone with
retarded correlators in specially designed states. Furthermore, we study the
temperature dependence of the logarithmic light cone using out-of-time-ordered
correlators.
