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We study the time-dependent transmission of entanglement entropy through anout-of-equilibrium model interacting device in a quantum transport set-up. Thedynamics is performed via the Kadanoff-Baym equations within many-bodyperturbation theory. The double occupancy $< \hat{n}_{R \uparrow} \hat{n}_{R\downarrow} >$, needed to determine the entanglement entropy, is obtained fromthe equations of motion of the single-particle Green's function. A remarkableresult of our calculations is that $< \hat{n}_{R \uparrow} \hat{n}_{R\downarrow} >$ can become negative, thus not permitting to evaluate theentanglement entropy. This is a shortcoming of approximate, and yet conserving,many-body self-energies. Among the tested perturbation schemes, the $T$-matrixapproximation stands out for two reasons: it compares well to exact results inthe low density regime and it always provides a non-negative $< \hat{n}_{R\uparrow} \hat{n}_{R \downarrow} >$. For the second part of this statement, wegive an analytical proof. Finally, the transmission of entanglement across thedevice is diminished by interactions but can be amplified by a current flowingthrough the system.

Can we always get the entanglement entropy from the Kadanoff-Baym equations? The case of the T-matrix approximation