The only entanglement quantity is concurrence in a 2-qubit pure state. The maximum violation of Bells inequality is monotonically increasing for this quantity. Therefore, people expect that pure state entanglement is relevant to the quantum violation. To understand the relation between violation and entanglement, we extend the study to three qubits. We consider all possible 3-qubit operators with a symmetric permutation. When only turning on one entanglement measure, the numerical result shows a contradiction to the expectation. The maximum violation does not have the same behavior as in 2-qubit pure states. Therefore, we conclude Violation$ eq$Quantum. In the end, we propose the generalized $R$-matrix or correlation matrix for the new diagnosis of Quantum Entanglement. We demonstrate the evidence by restoring the monotonically increasing result.
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