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

Mutual information-energy inequality for thermal states of a bipartite quantum system