Universal time scaling for Hamiltonian parameter estimation

TL;DR

This paper demonstrates that incorporating optimal coherent feedback controls restores the intuitive notion that longer measurement times improve Hamiltonian parameter estimation precision, establishing a universal time scaling limit.

Contribution

It derives asymptotically optimal feedback controls and quantifies their maximal improvement, revealing a universal time scaling in Hamiltonian parameter estimation.

Findings

Optimal feedback controls enhance estimation precision.

Universal time scaling law established under feedback.

Feedback can counteract previously observed limitations.

Abstract

Time is a valuable resource and it seems intuitive that longer time should lead to better precision in Hamiltonian parameter estimation. However recent studies have put this intuition into question, showing longer time may even lead to worse estimation in certain cases. Here we show that the intuition can be restored if coherent feedback controls are included. By deriving asymptotically optimal feedback controls we present a quantification of the maximal improvement feedback controls can provide in Hamiltonian parameter estimation and show a universal time scaling for the precision limit of Hamiltonian parameter estimation under the optimal feedback scheme.