  Majorana qubits offer a promising way to store and manipulate quantum
information by encoding it into the state of Majorana zero modes. As the
information is stored in a topological property of the system, local noise
cannot lead to decoherence. Manipulation of the information is achieved by
braiding the zero modes. The measurement, however, is challenging as the
information is well hidden and thus inherently hard to access. Here, we discuss
a setup for measuring the state of a Majorana qubit by employing standard tools
of microwave engineering. The basic physical effect that we employ is the fact
that a voltage-biased Josephson junction hosting Majorana fermions allows
photons to be emitted and absorbed at half the Josephson frequency. We show
that in the dispersive regime, our setup allows us to perform a quantum
nondemolition measurement and to reach the quantum limit. An appealing feature
of our setup is that the interaction of the Majorana qubit with the measurement
device can be turned on and off at will by changing the dc bias of the
junction.
