We investigate the entanglement dynamics in a free-fermion chain initially
prepared in a Fermi sea and subjected to
localized losses (dissipative impurity). We derive a formula describing the dynamics
of the entanglement entropies in
the hydrodynamic limit of long times and large intervals.
The result depends only on the absorption coefficient of the effective
delta potential describing the impurity in the hydrodynamic limit.
Genuine dissipation-induced entanglement is certified by
the linear growth of the logarithmic negativity.
Finally, in the quantum Zeno regime at strong dissipation the entanglement growth is
arrested (Zeno entanglement death).