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Gaussian tripartite entanglement out of equilibrium

The stationary multipartite entanglement between three interacting harmonic oscillators subjected to decoherence is analyzed in the largely unexplored non-equilibrium strong dissipation regime. We compute the exact asymptotic Gaussian state of the system and elucidate its separability properties, qualitatively assessing the regions of the space of parameters in which fully inseparable states are generated. Interestingly, the sharing structure of bipartite entanglement is seen to degrade as dissipation increases even for very low temperatures, at which the system approaches its ground state. We also find that establishing stationary energy currents across the harmonic chain does not correspond with the build-up of biseparable steady states, which relates instead just to the relative intensity of thermal fluctuations.