Is the average of the spin-correlation elements the real measure of the entanglement of the two-qubit systems?

TL;DR

This paper introduces a spin-correlation matrix-based criterion for assessing entanglement in two-qubit systems, which aligns with concurrence results and applies to both pure and mixed states.

Contribution

It proposes a new, generic criterion based on the spin-correlation matrix for detecting entanglement in two-qubit systems, applicable to mixed and multipartite states.

Findings

The criterion agrees with concurrence in various examples.

It is necessary and sufficient for full correlation.

Applicable to mixed and pure states, extendable to multipartite systems.

Abstract

Based on the Pauli spin operators we develop the notion of the spin-correlation matrix for the two-qubit system. If this matrix is non-zero, the measure of the correlation between the qubits is the average of the non-zero elements. Trivially, for zero matrix the bipartite is uncorrelated. This criterion turns out to be a necessary and sufficient condition for the full correlation, where it includes information on both entanglement and correlation other than entanglement. Moreover, we discuss to what extent this criterion can give information on the entanglement of the system. The criterion is generic in the sense that it can be applied to mixed and pure systems. Also, it can be easily extended to treat the correlation of multipartite systems. We compare the results obtained from this criterion to those from concurrence for various examples and we gain agreement regarding entanglement. We believe that this criterion may have a wide range of potential applications in quantum information theory.