Quantum speed limit time of a spin qubit in noninteracting spin bath

We study the dynamic of quantum speed limit (QSL) time of a qubit coupled to a bath of noninteracting spins. The investigations are carried under both exact and approximate solutions of the model and the results of the two approaches are compared with each other. Under the exact solution and in the low temperature limit, QSL time becomes independent of the number of spins in the environment with potential capacity for quantum speed up. Beyond a critical value of temperature, there exists a frequency of the spins that reduces the capacity for speeding up quantum evolution. The effects of driving time, nonuniform frequencies of the bath's spins and coupling strength on QSL time are also investigated.