  This thesis addresses problems in the field of quantum information theory.
The first part of the thesis is opened with concrete definitions of general
quantum source models and their compression, and each subsequent chapter
addresses the compression of a specific source model as a special case of the
initially defined general models. First, we find the optimal compression rate
of a general mixed state source which includes as special cases all the
previously studied models such as Schumacher's pure and ensemble sources and
other mixed state ensemble models. For an interpolation between the visible and
blind Schumacher's ensemble model, we find the optimal compression rate region
for the entanglement and quantum rates. Later, we study the classical-quantum
variation of the celebrated Slepian-Wolf problem and the ensemble model of
quantum state redistribution for which we find the optimal compression rate
considering per-copy fidelity and single-letter achievable and converse bounds
matching up to continuity of functions which appear in the corresponding
bounds.
  The second part of the thesis revolves around information theoretical
perspective of quantum thermodynamics. We start with a resource theory point of
view of a quantum system with multiple non-commuting charges. Subsequently, we
apply this resource theory framework to study a traditional thermodynamics
setup with multiple non-commuting conserved quantities consisting of a main
system, a thermal bath and batteries to store various conserved quantities of
the system. We state the laws of the thermodynamics for this system, and show
that a purely quantum effect happens in some transformations of the system,
that is, some transformations are feasible only if there are quantum
correlations between the final state of the system and the thermal bath.
