We provide an analytical solution from the correlators of the generalized
R-matrix in the 3-qubit pure states. It provides the upper bound to the
maximum violation of Mermin's inequality. For a generic 2-qubit pure state, the
concurrence characterizes the maximum violation of Bell's inequality from the
R-matrix. Therefore, people expect that the maximum violation should be
proper to quantify Quantum Entanglement. The R-matrix shows the maximum
violation of Bell's operator. For a general 3-qubit state, we have five
invariant entanglement quantities under local unitary transformations. We show
that the five invariant quantities describe the correlation in the generalized
R-matrix. The violation of Mermin's operator is not a proper diagnosis by
observing the dependence for entanglement measures. We then classify 3-qubit
quantum states. Each classification quantifies Quantum Entanglement by the
total concurrence. In the end, we relate the experiment correlators to Quantum
Entanglement.Comment: 14 pages, 4 figures, minor changes, reference change