  Robust zero bias transport anomalies in semiconducting nanowires with
proximity-induced superconductivity have been convincingly demonstrated in
various experiments. While these are compatible with the existence of Majorana
zero modes at the ends of the nanowire, a direct proof of their non-locality
and topological protection is now needed. Here we show that a quantum dot at
the end of the nanowire may be used as a powerful spectroscopic tool to
quantify the degree of Majorana non-locality through a local transport
measurement. Moreover, the spin polarization of dot sub-gap states at
singlet-doublet transitions in the Coulomb blockade regime allows the dot to
directly probe the spin structure of the Majorana wave function, and indirectly
measure the spin-orbit coupling of the nanowire.
