Quantum parameter estimation affected by unitary disturbance

TL;DR

This paper develops a general framework to analyze how unitary disturbances impact quantum parameter estimation, showing that such disturbances cannot improve estimation precision and that external fields do not always degrade it.

Contribution

It provides an analytical expression for quantum Fisher information under unitary disturbances, revealing fundamental limits on estimation precision in disturbed quantum systems.

Findings

Optimal estimation precision cannot be surpassed by adding unitary disturbances.

Increasing external field strength does not necessarily reduce estimation accuracy.

Analytical formula for quantum Fisher information in disturbed dynamics.

Abstract

We provide a general framework for handling the effects of a unitary disturbance on the estimation of the amplitude $\lambda$ associated to a unitary dynamics. By computing an analytical and general expression for the quantum Fisher information, we prove that the optimal estimation precision for $\lambda$ cannot be outperformed through the addition of such a unitary disturbance. However, if the dynamics of the system is already affected by an external field, increasing its strength does not necessary imply a loss in the optimal estimation precision.