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Using the expression of the fidelity for the most general Gaussian quantumstates, the quantum fidelity is studied for the states of a harmonic oscillatorinteracting with an environment, in particular with a thermal bath. The timeevolution of the considered system is described in the framework of the theoryof open systems based on quantum dynamical semigroups. By taking a correlatedsqueezed Gaussian state as initial state, we calculate the quantum fidelity forboth undisplaced and displaced states. The time evolution of the quantumfidelity is analyzed depending on the squeezing and correlation parameterscharacterizing the initial Gaussian state and on the dissipation constant andtemperature of the thermal bath.

Quantum fidelity for Gaussian states describing the evolution of open systems