Fundamental limits of non-Hermitian sensing from quantum Fisher information

Abstract

Exceptional points (EPs) exhibit strongly enhanced spectral responses and are therefore promising candidates for sensing applications. Whether these non-Hermitian degeneracies provide a genuine advantage in the quantum regime has been the subject of ongoing debate. Here, we address this issue within a scattering-matrix formalism for sensing with coherent light, which allows the quantum Fisher information (QFI) to be evaluated directly from experimentally accessible scattering data without introducing additional noise channels beyond those inherent to the scattering process. We analyze both nondegenerate and degenerate scattering-matrix poles, including EPs of arbitrary order, and show that the QFI per incoming photon flux is bounded and controlled by three key factors: the decay rate of the resonant mode, the strength of the spectral response associated with non-normality, and the adjustment between the scattering states and the information source. For spatially localized perturbations, this implies that the maximal QFI achievable by wavefront shaping is fully determined by the local density of states at the perturbation site. Within this framework, we demonstrate that EPs can enhance the QFI compared to isolated modes or diabolic points with identical decay rates, and that the QFI can be further increased by moving away from the EP toward parameter regimes where non-Hermitian linewidth splitting reduces the decay rate of one mode. We further show that sufficiently small additional internal losses do not alter this overall picture, thereby providing a unified and experimentally relevant perspective on the design of quantum-limited non-Hermitian sensors.