  Chaotic dynamics in closed local quantum systems scrambles quantum
information, which is manifested quantitatively in the decay of the
out-of-time-ordered correlators (OTOC) of local operators. How is information
scrambling affected when the system is coupled to the environment and suffers
from dissipation? In this paper, we address this question by defining a
dissipative version of OTOC and numerically study its behavior in a
prototypical chaotic quantum chain in the presence of dissipation. We find that
dissipation leads to not only the overall decay of the scrambled information
due to leaking, but also structural changes so that the `information light
cone' can only reach a finite distance even when the effect of overall decay is
removed. Based on this observation we conjecture a modified version of the
Lieb-Robinson bound in dissipative systems.
