Quantum Fidelity of Two-mode Gaussian States in a Uniform Magnetic Field

In the framework of the theory of open quantum systems, we investigate the quantum fidelity for a two-mode system consisting of uncoupled harmonic oscillators which interacts with a thermal bath as the environment. We take the coherent states of a spineless charged particle in an anisotropic harmonic potential and a uniform magnetic field as initial Gaussian states of the considered system and describe the dependence of fidelity. The evolution of the Uhlmann quantum fidelity of this Gaussian state shows that quantum fidelity takes always only non-zero values.