In this work, we study the system formed by two coupled harmonic oscillators in
three situations: in the absence of an environment; both interacting with a
thermal bath; and only one of the oscillators interacting with the bath. We
evaluated quantities of interest to the field of Quantum Information, such as
entanglement, coherence and fidelity. In the absence of the environment, the
squeezing parameter μ directly influences the entanglement increase, while the
parameter λ, which regulates the exchange of excitations between the
oscillators, affects the coherence of one of the modes. The time evolution of the
system reveals that these quantities remain unchanged. When both oscillators
interact with the environment, the squeezing between them decreases, which
leads to a weakening of the entanglement. There is a threshold temperature
after which the entanglement completely disappears. In the situation where only
one of the oscillators interacts with the bath, the coherence and fidelity present
an oscillatory behavior that strongly depends on parameter λ. This evidences a
system memory effect. We attribute this behavior exclusively to the coupling
between the oscillators, since we consider a Markovian dynamic for the system
in the presence of the environment.