  Entanglement detection is an important problem in quantum information theory
because quantum entanglement is a key resource in quantum information
processing. Realignment criteria is a powerful tool for detection of entangled
states in bipartite and multipartite quantum system. It is an important
criteria for entanglement detection because it works well; not only for
negative partial transpose entangled states (NPTES) but also for positive
partial transpose entangled states (PPTES). Since the matrix corresponding to
realignment map is indefinite so the experimental implementation of the map is
an obscure task. In this work, firstly, 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.
Moreover, we have analysed the error that may occur because of approximating
the realignment map.
