  We investigated the quantum speed limit time of a qubit system with
non-Hermitian detuning. Our results show that, with respect to two
distinguishable states of the non-Hermitian system, the evolutionary time does
not have a nonzero lower bound. And the quantum evolution of the system can be
effectively accelerated by adjusting the non-Hermitian detuning parameter, as
well as the quantum speed limit time can be arbitrarily small even be zero.
