  We discuss the known construction of two interacting superconducting
circuits, based on Josephson junctions, that can be precisely engineered and
easily controlled. In particular, we use the parametric excitation of two
circuits, realized by an instant change of the qubit coupling, to study
entropic and information properties of the density matrix of the composite
system. The density matrix is obtained from the initial thermal state and is
then analyzed in the approximation of small perturbation parameter and
sufficiently low temperature. We also check the subadditivity condition for
this system both for von Neumann and deformed entropies and look at the
dependance of mutual information on the temperature of the system. Finally, we
discuss the applicability of this approach to describe such system of two
coupled superconducting qubits as harmonic oscillators with limited Hilbert
space.
