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Abstract
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We describe the dynamics of entanglement of three-mode Gaussian states of
a system composed of three bosonic modes, each one immersed in its own thermal
reservoir, in the framework of the theory of open systems based on completely positive
quantum dynamical semigroups. By using the criteria for the separability of three-mode
systems, we classify the states by different values of the parameters characterizing the
system and the thermal reservoirs. We consider a fully inseparable state as an initial
state and show that for definite values of temperature and dissipation constants, the class
of entanglement to which the state of the system belongs is changing during its time
evolution. For all non-zero values of temperatures of the thermal baths, suppression of
entanglement of the initial state always takes place, and in the limit of large times the
state is fully separable, corresponding to an asymptotic product state.
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