Entanglement witnessing in superconducting beamsplitters

We analyse a large class of superconducting beamsplitters for which the Bell parameter (CHSH violation) is a simple function of the spin detector efficiency. For these superconducting beamsplitters all necessary information to compute the Bell parameter can be obtained in Y-junction setups for the beamsplitter. Using the Bell parameter as an entanglement witness, we propose an experiment which allows to verify the presence of entanglement in Cooper pair splitters.