Quantum Speed Limit Time of A Spin Qubit Coupled With Heisenberg Spin Environment

We investigated the quantum speed limit (QSL) time of a spin qubit coupled to an XXZ Heisenberg spin chain environment. The spins of the environment are coupled to the system qubit through Heisenberg like interaction. We carried out our investigations under approximate solution and we evaluate the minimal evolution time from initial state to one of its final target state. QSL time becomes uniform in the low temperature limit and at higher temperature different oscillatory behaviors are observed. Maximal speed of evolution of quantum systems is determined by QSL time. We use Margolus-Levitin (ML) types bound to investigate the minimal evolution time of quantum states. We also discuss the dependence of QSL time upon temperature, driving time and anisotropy of spin chain environment.