Quality of correlation in quantum information

A strong and stable correlation in quantum information is of high quality for quantum information processing. We define two quantities, selective average correlation and ripple coefficient, to evaluate the quality of correlation in quantum information in a time interval. As a new communication channel, Heisenberg spin chains are widely investigated. We select a two-qubit Heisenberg XXZ spin chain with Dzyaloshinskii-Moriya interaction in an inhomogeneous magnetic field as an example, and use the two quantities to evaluate the qualities of the correlation in quantum information with different measures. The result shows that, if the time evolutions are similar, there needs only evaluating one of them to know when the correlation has high quality for quantum information processing.