  The generation of spin-entangled electrons is an important prerequisite for
future solid-state quantum technologies. Cooper pairs in a superconductor can
be split into separate electrons in a spin-singlet state, however, detecting
their entanglement remains an open experimental challenge. Proposals to detect
the entanglement by violating a Bell inequality typically require a large
number of current cross-correlation measurements, and not all entangled states
can be detected in this way. Here, we instead formulate an entanglement witness
that can detect the spin-entanglement using only three cross-correlation
measurements of the currents in the outputs of a Cooper pair splitter. We
identify the optimal measurement settings for witnessing the entanglement, and
we illustrate the use of our entanglement witness with a realistic model of a
Cooper pair splitter for which we evaluate the cross-correlations of the output
currents. Specifically, we find that the entanglement of the spins can be
detected even with a moderate level of decoherence. Our work thereby paves the
way for an experimental detection of the entanglement produced by Cooper pair
splitters.
