  Quantum channels, also called quantum operations, are linear, trace
preserving and completely positive transformations in the space of quantum
states. Such operations describe discrete time evolution of an open quantum
system interacting with an environment. The thesis contains an analysis of
properties of quantum channels and different entropies used to quantify the
decoherence introduced into the system by a given operation. Part I of the
thesis provides a general introduction to the subject. In Part II, the action
of a quantum channel is treated as a process of preparation of a quantum
ensemble. The Holevo information associated with this ensemble is shown to be
bounded by the entropy exchanged during the preparation process between the
initial state and the environment. A relation between the Holevo information
and the entropy of an auxiliary matrix consisting of square root fidelities
between the elements of the ensemble is proved in some special cases. Weaker
bounds on the Holevo information are also established. The entropy of a
channel, also called the map entropy, is defined as the entropy of the state
corresponding to the channel by the Jamiolkowski isomorphism. In Part III of
the thesis, the additivity of the entropy of a channel is proved. The minimal
output entropy, which is difficult to compute, is estimated by an entropy of a
channel which is much easier to obtain. A class of quantum channels is
specified, for which additivity of channel capacity is conjectured. The last
part of the thesis contains characterization of Davies channels, which
correspond to an interaction of a state with a thermal reservoir in the week
coupling limit, under the condition of quantum detailed balance and
independence of rotational and dissipative evolutions. The Davies channels are
characterized for one-qubit and one-qutrit systems.
