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Detection and classification of entanglement properties of a multi-qubitsystem is a topic of great interest. This topic has been studied extensivelyand thus we found different approaches for the detection and classification ofmulti-qubit entangled states. We have applied partial transposition operationon one of the qubit of the three-qubit system and then studied the entanglementproperties of the three-qubit system, which is under investigation. Since thepartial transposition operation is not a quantum operation so we haveapproximated partial transposition operation in such a way so that it representa completely positive map. The approximated partial transposition operation isalso known as structural physical approximation of partial transposition(SPA-PT). We have studied in detail the application of SPA-PT on a three qubitsystem and provided explicitly the matrix elements of the density matrixdescribing SPA-PT of a three qubit system. Moreover, we propose criterion toclassify all possible stochastic local operations and classicalcommunication(SLOCC) inequivalent classes of a pure as well as mixed threequbit state through SPA-PT map, which makes our criterion experimentallyrealizable. We have illustrated our criterion for detection and classificationof three-qubit entangled states by considering few examples.

the european physical journal. d, atomic, molecular and optical physics/the european physical journal. d, atomic, molecular, optical and plasma physics

Structural physical approximation of partial transposition makes possible to distinguish SLOCC inequivalent classes of three-qubit system