Direct measure of quantum correlation

The quantumness of the correlation known as quantum correlation is usually measured by quantum discord. So far various quantum discords can be roughly understood as indirect measure by some special discrepancy of two quantities. We present a direct measure of quantum correlation by revealing the difference between the structures of classically and quantum correlated states. Our measure explicitly includes the contributions of the inseparability and local nonorthogonality of the eigenvectors of a density matrix. Besides its relatively easy computability, our measure can provide a unified understanding of quantum correlation of all the present versions.

Figure 1

(Dimensionless) Quantum correlations based on various definitions versus $a$. The dash-dotted line corresponds to the quantum correlation defined by Theorem 1. The solid line corresponds to the strictly quantum correlation given by Theorem 3 and meanwhile it also corresponds to the quantum correlation subject A defined by Eq. (9). The “o” line corresponds to the simplified strictly quantum correlation given by Theorem 5. The dashed line is the quantum correlation subject to A given by the authors of Ref. [26]