  Schemes for topological quantum computation with Majorana bound states rely
heavily on the ability to measure products of Majorana operators projectively.
Here, we employ Markovian quantum measurement theory, including the readout
device, to analyze such measurements. Specifically, we focus on the readout of
Majorana qubits via continuous charge sensing of a tunnel-coupled quantum dot
by a quantum point contact. We show that projective measurements of Majorana
products $\prod_i\hat{\gamma}_i$ can be implemented by continuous charge
sensing under quite general circumstances. Essential requirements are that a
combined local parity $\hat{\pi}$, involving the quantum dot charge along with
the Majorana product of interest, be conserved, and that the two eigenspaces of
the combined parity $\hat{\pi}$ generate distinguishable measurement signals.
We find that qubit readout may have to rely on measuring noise correlations of
the quantum-point-contact current. The average current encodes the qubit
readout only transiently for fine-tuned parameters or in the presence of
relaxation processes. We also discuss the corresponding measurement and
decoherence times and consider processes such as residual Majorana
hybridizations which are detrimental to the measurement protocol. Finally, we
emphasize that the underlying mechanism -- which we term symmetry-protected
readout -- is quite general and has further implications for both, Majorana and
non-Majorana systems.
