  Characterization of mixed quantum states represented by density operator is
one of the most important task in quantum information processing. In this work
we will present a geometric approach to characterize the density operator in
terms of fiber bundle over a quantum phase space. The geometrical structure of
the quantum phase space of an isospectral mixed quantum states can be realized
as a co-adjoint orbit of a Lie group equipped with a specific K\"{a}hler
structure.
  In particular we will briefly discuss the construction of a fiber bundle over
the quantum phase space based on symplectic reduction and purification method.
We will also show that the map is a Riemannian submersion which enable us to
provide some applications of the geometric framework such as geometric phase
and quantum speed limit.
