Quantum Metrological Limits via a Variational Approach

TL;DR

This paper introduces a variational method to compute quantum Fisher information in noisy systems, providing analytical bounds on phase estimation precision affected by noise.

Contribution

It presents a new variational equation for quantum Fisher information that explicitly accounts for noise, enabling better bounds on quantum measurement precision.

Findings

Derived an explicit variational equation for quantum Fisher information in noisy systems

Obtained analytical bounds on phase estimation precision under phase diffusion

Showed that noise imposes a fundamental limit on measurement accuracy

Abstract

The minimum achievable statistical uncertainty in the estimation of physical parameters is determined by the quantum Fisher information. Its computation for noisy systems is still a challenging problem. Using a variational approach, we present an equation for obtaining the quantum Fisher information, which has an explicit dependence on the mathematical description of the noise. This method is applied to obtain a useful analytical bound to the quantum precision in the estimation of phase-shifts under phase diffusion, which shows that the estimation uncertainty cannot be smaller than a noise-dependent constant.