  The observation of zero-bias conductance peaks in vortex cores of certain
Fe-based superconductors has sparked renewed interest in vortex-bound Majorana
states. These materials are believed to be intrinsically topological in their
bulk phase, thus avoiding potentially problematic interface physics encountered
in superconductor-semiconductor heterostructures. However, progress toward a
vortex-based topological qubit is hindered by our inability to measure the
topological quantum state of a non-local vortex Majorana state, i.e., the
charge of a vortex pair. In this paper, we theoretically propose a
microwave-based charge parity readout of the Majorana vortex pair charge. A
microwave resonator above the vortices can couple to the charge allowing for a
dispersive readout of the Majorana parity. Our technique may also be used in
vortices in conventional superconductors and allows one to probe the lifetime
of vortex-bound quasiparticles, which is currently beyond existing scanning
tunneling microscopy capabilities.
