  The unique entanglement measure is concurrence in a 2-qubit pure state. The
maximum violation of Bell's inequality is monotonically increasing for this
quantity. Therefore, people expect that pure state entanglement is relevant to
the non-locality. For justification, we extend the study to three qubits. We
consider all possible 3-qubit operators with a symmetric permutation. When only
considering one entanglement measure, the numerical result contradicts
expectation. Therefore, we conclude ``Non-Locality$\neq$Quantum Entanglement''.
We propose the generalized $R$-matrix or correlation matrix for the new
diagnosis of Quantum Entanglement. We then demonstrate the evidence by
restoring the monotonically increasing result.
