  Distinct from closed quantum systems, non-Hermitian system can have
exceptional points (EPs) where both eigenvalues and eigenvectors coalesce.
Recently, it has been proposed and demonstrated that EPs can enhance the
performance of sensors in terms of amplification of detected signal. Meanwhile,
the noise might also be amplified at EPs and it is not obvious whether
exceptional points will still improve the performance of sensors when both
signal and noise are amplified. We develop quantum noise theory to
systematically calculate the signal and noise associated with the EP sensors.
We then compute quantum Fisher information to extract a lower bound of the
sensitivity of EP sensors. Finally, we explicitly construct an EP sensing
scheme based on heterodyne detection to achieve the same scaling of the
ultimate sensitivity with enhanced performance. Our results can be generalized
to higher order EPs for any bosonic non-Hermitian system with linear
interactions.
