Quantum Correlations:Geometry and Applications

In the studies of quantum information and computation, the quantum correlations present in a non-classical system are seen as natural resources. In this thesis, we present a detailed study on quantification and characterization of multipartite quantum entanglement from a geometric perspective. Furthermore, we present protocols and algorithms where quantum correlations such as entanglement, quantum Fisher information, and quantum superposition have been used to provide advantages as well securities in quantum communication tasks, quantum speed-up, and protection against the decoherence in an open quantum system. First, we use a geometric measure of entanglement quantification based on Euclidean distance of the Hermitian matrices to obtain the minimum distance between the set of bipartite n- qudit density matrices with a positive partial transpose and the maximally mixed state. This minimum distance coincides with the radius of the largest separable ball. We present the interior geometry of the set of all positive semidefinite matrices and identify a particular class of Werner states for which the Peres-Horodecki criterion is both necessary and sufficient for separability even in the dimensions greater than six.