Quantum speed limits of quantum system in colored environments

In this paper, we investigate quantum speed limits (QSLs) of a two -level system in the colored environments which are described by stochastic processes. We present QSL can be affected by the correlation time, the partitions of the constituent elements of the two -level system in different colored environments: the Ornstein-Uhlenbeck environment, simple fluctuating bottleneck environment, and the Dichotomic (two -state) environment. The investigations provide us a potential way to manipulate the quantum speed limit time (QSLT) of the quantum system in the colored environments. Our results could provide different insights on quantum control technologies of QSL and decoherent dynamics for the quantum computation.