Algebraic metrology: Pretty good states and bounds

TL;DR

This paper explores quantum metrology using Lie algebra techniques to identify highly symmetric states that achieve Heisenberg scaling, analyzing their performance under noise through numerical and theoretical bounds.

Contribution

It introduces a Lie algebraic framework to construct states with optimal precision scaling and evaluates their robustness against noise in quantum metrology.

Findings

Identifies states with Heisenberg scaling in noiseless conditions.

Derives upper bounds on quantum Fisher information under noise.

Performs numerical analysis of state performance in noisy environments.

Abstract

We investigate quantum metrology using a Lie algebraic approach for a class of Hamiltonians, including local and nearest-neighbor interaction Hamiltonians. Using this Lie algebraic formulation, we identify and construct highly symmetric states that admit Heisenberg scaling in precision in the absence of noise, and investigate their performance in the presence of noise. To this aim we perform a numerical scaling analysis, and derive upper bounds on the quantum Fisher information.