Employing the Pauli matrices, we have constructed a set of operators, which can be used to distinguish six inequivalent classes of entanglement under SLOCC (stochastic local operation and classical communication) for three-qubit pure states. These operators have very simple structure and can be obtained from the Mermins operator with suitable choice of directions. Moreover these operators may be implemented in an experiment to distinguish the types of entanglement present in a state. We show that the measurement of only one operator is sufficient to distinguish GHZ class from rest of the classes. It is also shown that it is possible to detect and classify other classes by performing a small number of measurements. We also show how to construct such observables in any basis. We also consider a few mixed states to investigate the usefulness of our operators. Furthermore, we consider the teleportation scheme of Lee et al. (Phys. Rev. A 72, 024302 (2005)) and show that the partial tangles and hence teleportation fidelity can be measured. We have also shown that these partial tangles can also be used to classify genuinely entangled state, biseparable state and separable state.
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