  A short superconducting segment can couple attached quantum dots via elastic
co-tunneling (ECT) and crossed Andreev reflection (CAR). Such coupled quantum
dots can host Majorana bound states provided that the ratio between CAR and ECT
can be controlled. Metallic superconductors have so far been shown to mediate
such tunneling phenomena, albeit with limited tunability. Here we show that
Andreev bound states formed in semiconductor-superconductor heterostructures
can mediate CAR and ECT over mesoscopic length scales. Andreev bound states
possess both an electron and a hole component, giving rise to an intricate
interference phenomenon that allows us to tune the ratio between CAR and ECT
deterministically. We further show that the combination of intrinsic spin-orbit
coupling in InSb nanowires and an applied magnetic field provides another
efficient knob to tune the ratio between ECT and CAR and optimize the amount of
coupling between neighboring quantum dots.
