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Abstract
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In the framework of the theory of open systems based on completely
positive quantum dynamical semigroups, we describe the evolution of the Uhlmann
quantum fidelity of a pair of two-mode Gaussian states, for a system consisting of two
non-interacting bosonic modes embedded in two independent thermal environments.
We take entangled squeezed thermal states as initial states of the considered system and
describe the dependence of fidelity, which is fully determined by the covariance matrix,
on time and temperatures of thermal reservoirs. We also present the explicit expression
of the fidelity at infinity of time as a function of temperatures of the two reservoirs,
squeezing parameter and average numbers of thermal photons, and show that quantum
fidelity takes always only non-zero values.
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