  Using the expression of the fidelity for the most general Gaussian quantum
states, the quantum fidelity is studied for the states of a harmonic oscillator
interacting with an environment, in particular with a thermal bath. The time
evolution of the considered system is described in the framework of the theory
of open systems based on quantum dynamical semigroups. By taking a correlated
squeezed Gaussian state as initial state, we calculate the quantum fidelity for
both undisplaced and displaced states. The time evolution of the quantum
fidelity is analyzed depending on the squeezing and correlation parameters
characterizing the initial Gaussian state and on the dissipation constant and
temperature of the thermal bath.
