Tripartite Entanglement and Quantum Correlation

TL;DR

This paper analytically explores tripartite entanglement and quantum correlations using the generalized R-matrix, revealing limitations of Mermin's inequality violation as an entanglement measure and proposing a classification based on invariant quantities.

Contribution

It introduces an analytical framework connecting the generalized R-matrix with tripartite entanglement invariants and classifies 3-qubit states based on total concurrence.

Findings

Maximum violation of Mermin's inequality is not a reliable entanglement measure.

Five invariant quantities describe correlations in the generalized R-matrix.

A classification scheme for 3-qubit states based on total concurrence.

Abstract

We provide an analytical tripartite-study from the generalized $R$-matrix. It provides the upper bound of the maximum violation of Mermin's inequality. For a generic 2-qubit pure state, the concurrence or $R$-matrix characterizes the maximum violation of Bell's inequality. Therefore, people expect that the maximum violation should be proper to quantify Quantum Entanglement. The $R$-matrix gives the maximum violation of Bell's inequality. For a general 3-qubit state, we have five invariant entanglement quantities up to local unitary transformations. We show that the five invariant quantities describe the correlation in the generalized $R$-matrix. The violation of Mermin's inequality is not a proper diagnosis due to the non-monotonic behavior. 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.