Sequential feedback scheme outperforms the parallel scheme for Hamiltonian parameter estimation

TL;DR

This paper demonstrates that the sequential feedback scheme significantly outperforms the parallel scheme in quantum Hamiltonian parameter estimation, achieving up to threefold improvements and enabling simultaneous high-precision estimation of magnetic field components.

Contribution

It proves the superiority of the sequential feedback scheme over the parallel scheme for quantum Hamiltonian estimation and establishes a benchmark for multi-parameter magnetic field estimation.

Findings

Sequential feedback scheme achieves 3-fold improvement in 2D systems.

Order of $O(d+1)$ improvement in $d$-dimensional systems.

High-precision simultaneous estimation of all three magnetic field components.

Abstract

Measurement and estimation of parameters are essential for science and engineering, where the main quest is to find out the highest achievable precision with given resources and design schemes to attain it. Two schemes, the sequential feedback scheme and the parallel scheme, are usually studied in quantum parameter estimation. While the sequential feedback scheme represents the most general scheme, it remains unknown whether it can outperform the parallel scheme for any quantum estimation tasks. In this Letter we show that the sequential feedback scheme has a 3-fold improvement over the parallel scheme for Hamiltonian parameter estimations on 2-dimensional systems, and an order of $O(d+1)$ improvement for Hamiltonian parameter estimation on $d-$dimensional systems. We also show that, contrary to the conventional belief, it is possible to simultaneously achieve the highest precision for estimating all three components of a magnetic field, which sets a benchmark on the local precision limit for the estimation of a magnetic field.