  We study the effect of inelastic scattering on the spin entanglement
detection and discrimination scheme proposed by Egues, Burkard, and Loss [Phys.
Rev. Lett. \textbf{89}, 176401 (2002)]. The finite-backscattering beam splitter
geometry is supplemented by a phenomenological model for inelastic scattering,
the charge-conserving voltage probe model, conveniently generalized to deal
with entangled states. We find that the behavior of shot-noise measurements in
one of the outgoing leads remains an efficient way to characterize the nature
of the non-local spin correlations in the incoming currents for an inelastic
scattering probability up to 50%. Higher order cumulants are analyzed, and are
found to contain no additional useful information on the spin correlations. The
technique we have developed is applicable to a wide range of systems with
voltage probes and spin correlations.
