Fisher-information susceptibility for multiparameter quantum estimation

Year: 2024

Authors: Albarelli F., Gianani I., Genoni M.G., Barbieri M.

Autors Affiliation: Scuola Normale Super Pisa, I-56126 Pisa, Italy; Univ Roma Tre, Dipartimento Sci, Via Vasca Navale 84, I-00146 Rome, Italy; Univ Milan, Dept Phys A Pontremoli, I-20133 Milan, Italy; CNR, Ist Nazl Ott, Largo Enrico Fermi 6, I-50126 Florence, Italy.

Abstract: Noise affects the performance of quantum technologies, hence the importance of elaborating operative figures of merit that can capture its impact in exact terms. In quantum metrology, the introduction of the Fisher-information measurement noise susceptibility now allows one to quantify the robustness of measurement for single-parameter estimation. Here we extend this notion to the multiparameter quantum estimation scenario. We provide its mathematical definition in the form of a semidefinite program. Although a closed formula could not be found, we further derive an upper and a lower bound to the susceptibility. We then apply these techniques to two paradigmatic examples of multiparameter estimation: the joint estimation of phase and phase diffusion and the estimation of the different parameters describing the incoherent mixture of optical point sources. Our figure of merit provides clear indications on conditions allowing or hampering robustness of multiparameter measurements.

Journal/Review: PHYSICAL REVIEW A

Volume: 110 (3)      Pages from: 32436-1  to: 32436-11

More Information: We thank R. Demkowicz-Dobrzanski for discussions. M.B. and I.G. acknowledge support from the European Union (EU) Commission (H2020 FET-OPEN-RIA STORMY-TUNE, Grant No. 899587) , MUR Grant No. PRIN22-RISQUE-2022T25TR3 and Dipartimento di Eccellenza 2023-2027. M.G.G. acknowledges support from Italian Ministry of Research and Next Generation EU via the PRIN 2022 project CONTRABASS (Contract No. 2022KB2JJM) . F.A. acknowledges support from Marie Sklodowska-Curie Action EUHORIZON-MSCA-2021PF-01 (project QECANM, Grant No. 101068347) .
KeyWords: Fisher information; Information measurement; Mathematical definitions; Measurement Noise; Multiparameters; Parameters estimation; Performance; Quantum metrology; Quantum technologies; Single parameter
DOI: 10.1103/PhysRevA.110.032436