  We study the time-dependent transmission of entanglement entropy through an
out-of-equilibrium model interacting device in a quantum transport set-up. The
dynamics is performed via the Kadanoff-Baym equations within many-body
perturbation theory. The double occupancy $< \hat{n}_{R \uparrow} \hat{n}_{R
\downarrow} >$, needed to determine the entanglement entropy, is obtained from
the equations of motion of the single-particle Green's function. A remarkable
result of our calculations is that $< \hat{n}_{R \uparrow} \hat{n}_{R
\downarrow} >$ can become negative, thus not permitting to evaluate the
entanglement entropy. This is a shortcoming of approximate, and yet conserving,
many-body self-energies. Among the tested perturbation schemes, the $T$-matrix
approximation stands out for two reasons: it compares well to exact results in
the 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, we
give an analytical proof. Finally, the transmission of entanglement across the
device is diminished by interactions but can be amplified by a current flowing
through the system.
