  For some cavity-quantum-electrodynamics systems, such as a single electron
spin coupled to a passive cavity, it is challenging to reach the
strong-coupling regime. In such a weak-coupling regime, the conventional
dispersive readout technique cannot be used to resolve the quantum states of
the spin. Here we propose an improved dispersive readout method to measure the
quantum states of a weakly coupled qubit by harnessing either one or two
auxiliary cavities linearly coupled to the passive cavity containing the qubit.
With appropriate parameters in both cases, the system excluding the qubit can
exhibit a parity-time-symmetric phase transition at the exceptional point (EP).
Because the EP can amplify the perturbation induced by the qubit and the
parity-time symmetry can narrow the linewidths of the peaks in the transmission
spectrum of the passive cavity, we can measure the quantum states of the weakly
coupled qubit via this transmission spectrum. Owing to the weak coupling
between the qubit and the passive cavity, the backaction due to the measurement
of the qubit can also be reduced in comparison with the conventional dispersive
readout technique in the strong-coupling regime.
