Quantum Fisher Information of non-Hermitian sensing near exceptional points

Exceptional points are points in the parameter space of a non-hermitian system when two eigenvectors of the hamiltonian coalesce. Eigenvalue change of the non-hermitian system near exceptional points can have abnormal dependence on external perturbation, which is recently proposed and demonstrated as a way to enhance the sensitivity of resonant frequency shifts to small external signal. However, physical realization of non-hermitian system unavoidably introduces noises accompanying loss and gain to a hermitian system, which may potentially decrease the signal-to-noise ratio. To understand the combined effect of exceptional points on both sensitivity and signal-to-noise ratio, we computed the quantum fisher information of typical non-hermitian sensing processes, whose inverse give us a lower bound of the estimation error. Our work provides not only a fundamental bound for the sensing limit using exceptional points, but also a design tool to achieve the same scaling as the fundamental sensing limit.