Entanglement detection and quantification of entanglement are the two most important problems in quantum information theory because quantum entanglement is a key resource in quantum information processing. I will divide the talk into two parts: In the first part I will talk about realignment criterion, which is considered as powerful tool for detection of entangled states in bipartite and multipartite quantum system. It detects not only negative partial transpose entangled states (NPTES) but also detect positive partial transpose entangled states (PPTES). We have approximated the realignment map to a positive map using the method of structural physical approximation (SPA) and then we have shown that the structural physical approximation of realignment map (SPA-R) is completely positive. Positivity of the constructed map is characterized using moments which can be physically measured. Next, we develop a separability criterion based on our SPA-R map in the form of an inequality and have shown that the developed criterion not only detect NPTES but also PPTES. We have provided some examples to support the results obtained. In the second part, we define a physically realizable measure of entanglement for any arbitrary dimensional bipartite system ρ, which we named as structured negativity (NS(ρ)). We have shown that the introduced measure satisfies the properties of a valid entanglement monotone. For d ⊗ d dimensional state, we conjectured that negativity coincides with the structured negativity when the number of negative eigenvalues of the partially transposed matrix is equal to d(d−1)/2. Moreover, we proved that structured negativity may be implemented in the laboratory.
