  In this paper we investigate the dynamics of a spin chain whose two end spins
interact with two independent non-Markovian baths by using the non-Markovian
quantum state diffusion (QSD) equation approach. Specifically two issues about
quantum information scrambling in open quantum system are addressed. The first
issue is that tripartite mutual information (TMI) can quantify information
scrambling properly via its negative value in closed system, whether it is
still suitable to indicate quantum scrambling in open quantum system. However
we find that negative TMI is not an suitable quantifier of information
scrambling in open quantum system in some cases while negative tripartite
logarithmic negativity (TLN) is more appropriate. The second one is that up to
now almost all the open quantum system effects on information scrambling
reported were focus on the Markovian environment, while the effect of
non-Markovian environment on information scrambling is still elusive.
Significantly our results show that the memory effect of environment will be
beneficial to the emergence of quantum information scrambling. Moreover, it is
found that environment is generally detrimental for information scrambling in a
long time, while in some cases it will be helpful for information scrambling in
a short time.
