  In this work, we consider an upper bound for the quantum mutual information
in thermal states of a bipartite quantum system. This bound is related with the
interaction energy and logarithm of the partition function of the system. We
demonstrate the connection between this upper bound and the value of the mutual
information for the bipartite system realized by two spin-1/2 particles in the
external magnetic field with the XY-Heisenberg interaction.
