In this work, we use the formalism of Quantum Mechanics in the phase space
to study the system formed by two harmonic oscillators with position-position
coupling, interacting with a Markovian thermal bath. We calculate quantities of
interest in the field of Quantum Information such as, for example, coherence, fidelity,
mutual information and negativity of the Wigner function. In the presence of coupling
between the oscillators, the system coherence showed an oscillatory behavior, in a
given time interval, showing a memory effect of the system. We attribute this non-
monotonic coherence behavior exclusively to the coupling constant, as we consider
that the temporal evolution of the system, provided by the reservoir, was Markovian.