  We investigate the preparation of a target initial state for a two-level
(qubit) system from a system-environment equilibrium or correlated state by an
external field. The system-environment equilibrium or correlated state results
from the inevitable interaction of the system with its environment. An
efficient method in an extended auxiliary Liouville space is introduced to
describe the dynamics of the non-Markovian open quantum system in the presence
of a strong field and an initial system-environment correlation. By using the
time evolutions of the population difference, the state trajectory in the Bloch
sphere representation and the trace distance between two reduced system states
of the open quantum system, the effect of initial system-environment
correlations on the preparation of a system state is studied. We introduce an
upper bound and a lower bound for the trace distance within our perturbation
formalism to describe the diverse behaviors of the dynamics of the trace
distance between various correlated states after the system state preparation.
These bounds that are much more computable than similar bounds in the
literature give a sufficient condition and a necessary condition for the
increase of the trace distance and are related to the witnesses of
non-Markovianity and initial system-bath correlation.
