  Detection and classification of entanglement properties of a multi-qubit
system is a topic of great interest. This topic has been studied extensively
and thus we found different approaches for the detection and classification of
multi-qubit entangled states. We have applied partial transposition operation
on one of the qubit of the three-qubit system and then studied the entanglement
properties of the three-qubit system, which is under investigation. Since the
partial transposition operation is not a quantum operation so we have
approximated partial transposition operation in such a way so that it represent
a completely positive map. The approximated partial transposition operation is
also known as structural physical approximation of partial transposition
(SPA-PT). We have studied in detail the application of SPA-PT on a three qubit
system and provided explicitly the matrix elements of the density matrix
describing SPA-PT of a three qubit system. Moreover, we propose criterion to
classify all possible stochastic local operations and classical
communication(SLOCC) inequivalent classes of a pure as well as mixed three
qubit state through SPA-PT map, which makes our criterion experimentally
realizable. We have illustrated our criterion for detection and classification
of three-qubit entangled states by considering few examples.
