Geometric characterization of mixed quantum states

Abstract: 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.