  We investigate the spin entanglement in the superconductor-quantum dot system
proposed by Recher, Sukhorukov and Loss, coupling it to an electronic
beam-splitter. The superconductor-quantum dot entangler and the beam-splitter
are treated within a unified framework and the entanglement is detected via
current correlations. The state emitted by the entangler is found to be a
linear superposition of non-local spin-singlets at different energies, a
spin-entangled two-particle wavepacket. Colliding the two electrons in the
beam-splitter, the singlet spin-state gives rise to a bunching behavior,
detectable via the current correlators. The amount of bunching depends on the
relative positions of the single particle levels in the quantum dots and the
scattering amplitudes of the beam-splitter. The singlet spin entanglement,
insensitive to orbital dephasing but suppressed by spin dephasing, is
conveniently quantified via the Fano factors. It is found that the
entanglement-dependent contribution to the Fano factor is of the same magnitude
as the non-entangled, making an experimental detection feasible. A detailed
comparison between the current correlations of the non-local spin-singlet state
and other states, possibly emitted by the entangler, is performed. This
provides conditions for an unambiguous identification of the non-local singlet
spin entanglement.
