Optimal quantum discrimination at Liouvillian exceptional points

Abstract

Central to non-Hermitian sensing is the question of whether exceptional points (EPs) can make weak perturbations easier to detect. We show that despite enhanced spectral response, in finite-dimensional Lindblad systems with a unique stationary state and a nonzero relaxation gap, EPs offer no fundamental advantage in how the observation time required for reliable detection of a weak perturbation scales with the perturbation strength. We nevertheless demonstrate that by selectively choosing perturbations that enhance the quantum Fisher information rate, EPs can shorten the observation time needed to reach a predefined detection accuracy relative to a comparable non-EP reference at the same decay rate. As an illustration, we show using an optomechanical model at an EP that we can detect a weak force through the cavity output at the same reliability in less time than a non-EP reference. Our results establish fundamental limits on perturbation detection at EPs and can guide the design of faster non-Hermitian sensors based on optomechanical resonators, superconducting qubits, and trapped ions.