  Considering Rashba quantum wires with a proximity-induced superconducting gap
as physical realizations of Majorana fermions and quantum dots, we calculate
the overlap of the Majorana wave functions with the local wave functions on the
dot. We determine the spin-dependent tunneling amplitudes between these two
localized states and show that we can tune into a fully spin polarized
tunneling regime by changing the distance between dot and Majorana fermion.
Upon directly applying this to the tunneling model Hamiltonian, we calculate
the effective magnetic field on the quantum dot flanked by two Majorana
fermions. The direction of the induced magnetic field on the dot depends on the
occupation of the nonlocal fermion formed from the two Majorana end states
which can be used as a readout for such a Majorana qubit.
