title: Optimal feedback scheme and universal time scaling for Hamiltonian parameter estimation.
abstract: Time is a valuable resource and it is expected that a longer time period should lead to better precision in Hamiltonian parameter estimation. However, recent studies in quantum metrology have shown that in certain cases more time may even lead to worse estimations, which puts this intuition into question. In this Letter we show that by including feedback controls this intuition can be restored. By deriving asymptotically optimal feedback controls we quantify the maximal improvement feedback controls can provide in Hamiltonian parameter estimation and show a universal time scaling for the precision limit under the optimal feedback scheme. Our study reveals an intriguing connection between noncommutativity in the dynamics and the gain of feedback controls in Hamiltonian parameter estimation.
authors.affiliation: Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Shatin, Hong Kong.
authors.forename: Haidong
authors.initials: H
authors.lastname: Yuan
authors.affiliation: Canada Research Centre, Huawei Technologies Canada, Ontario, Canada; Huawei Noah's Ark Lab, Hong Kong Science Park, Shatin, Hong Kong.
authors.forename: Chi-Hang Fred
authors.initials: CH
authors.lastname: Fung