  This thesis presents studies performed on open quantum systems, that is,
quantum systems interacting with their surrounding environment. Such systems
are important not only in understanding the quantum-to-classical transition but
also for the practical implementation of modern quantum technologies. In
studies of open quantum systems performed to date, a very common assumption is
that the system and the environment are in separated initial states to begin
with. One primary objective of this thesis is to critically analyse this
assumption. We follow two different approaches to investigate the dynamics.
First, we solve an exactly solvable spin-spin model where a central spin system
interacts with a collection of quantum spins. We analyse exactly the central
spin dynamics, starting from both initially correlated and uncorrelated SE
states, and look at the dynamical differences due to the different starting
states. Second, we consider an arbitrary system interacting with an arbitrary
environment and derive a master equation that describes the system dynamics and
incorporates the effect of the initial SE correlations. This effect of initial
correlations is captured by an extra term appearing in the master equation. The
master equation is subsequently applied to the paradigmatic SE models such as
the spin-boson model and the spin-spin model. We demonstrate that the role
played by initial correlations can be noticeable even if the SE coupling
strength is kept smaller. The next part of the thesis deals with estimating the
parameters characterizing the environment of a quantum system where we show
that the use of two two-level systems can greatly enhance the estimation of the
environment parameters.
