  We present a way of identifying all kinds of entanglement for three-qubit
pure states in terms of the expectation values of Pauli operators. The
necessary and sufficient conditions to classify the fully separable,
biseparable, and genuine entangled states are explicitly given. The approach
can be generalized to multipartite high-dimensional cases. For three-qubit
mixed states, we propose two kinds of inequalities in terms of the expectation
values of complementary observables. One inequality has advantages in
entanglement detection of the quantum state with positive partial
transpositions, and the other is able to detect genuine entanglement. The
results give an effective method for experimental entanglement identification.
