Quantum information scrambling in non-Markovian open quantum systems

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.