  In this paper, we try to establish a connection between a quantum information
concept, i.e. the mutual information, and the conventional order parameter in
condensed matter physics. We show that a non-vanishing mutual information at a
long distance means the existence of long-range order. By analyzing the
entanglement spectra of the reduced density matrix that are used to calculate
the mutual information, we show how to find the local order operator used to
identify various phases with long-rang order.
