Tripartite Entanglement and Quantum Correlation

Abstract

We provide an analytical solution from the correlators of the generalized RR-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 RR-matrix. Therefore, people expect that the maximum violation should be proper to quantify Quantum Entanglement. The RR-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 RR-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

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