  Correlation function and mutual information are two powerful tools to
characterize the correlations in a quantum state of a composite system, widely
used in many-body physics and in quantum information science, respectively. We
find that these two tools may give different conclusions about the order of the
degrees of correlation in two specific two-qubit states. This result implies
that the orderings of bipartite quantum states according to the degrees of
correlation depend on which correlation measure we adopt.
