Measurement Noise Susceptibility in Quantum Estimation

Fisher information is a key notion in the whole field of quantum metrology. It allows for a direct quantification of the maximal achievable precision of the estimation of the parameters encoded in quantum states using the most general quantum measurement. It fails, however, to quantify the robustness of quantum estimation schemes against measurement imperfections, which are always present in any practical implementations. Here, we introduce a new concept of Fisher information measurement noise susceptibility that quantifies the potential loss of Fisher information due to small measurement disturbance. We derive an explicit formula for the quantity, and demonstrate its usefulness in the analysis of paradigmatic quantum estimation schemes, including interferometry and superresolution optical imaging.