  In order to assess inelastic effects on two fermion entanglement production,
we address an exactly solvable two-particle scattering problem where the target
is an excitable scatterer. Useful entanglement, as measured by the two particle
concurrence, is obtained from post-selection of oppositely scattered particle
states. The $S$ matrix formalism is generalized in order to address non-unitary
evolution in the propagating channels. We find the striking result that
inelasticity can actually increase concurrence as compared to the elastic case
by increasing the uncertainty of the single particle subspace. Concurrence
zeros are controlled by either single particle resonance energies or total
reflection conditions that ascertain precisely one of the electron states.
Concurrence minima also occur and are controlled by entangled resonance
situations were the electron becomes entangled with the scatterer, and thus
does not give up full information of its state. In this model, exciting the
scatterer can never fully destroy phase coherence due to an intrinsic limit to
the probability of inelastic events.
