Bounds on Quantum Multiple-Parameter Estimation with Gaussian State

TL;DR

This paper derives explicit quantum Fisher information bounds for multi-parameter estimation using Gaussian states, providing analytical tools to evaluate quantum limits in such estimation tasks.

Contribution

It introduces explicit formulas for quantum Fisher information matrices for Gaussian states, enabling precise bounds on multi-parameter quantum estimation.

Findings

Derived explicit right and symmetric logarithmic derivatives for Gaussian states.

Expressed quantum Fisher information matrices in terms of mean displacement and covariance.

Provided examples demonstrating the application of the analytical results.

Abstract

We investigate the quantum Cramer-Rao bounds on the joint multiple-parameter estimation with the Gaussian state as a probe. We derive the explicit right logarithmic derivative and symmetric logarithmic derivative operators in such a situation. We compute the corresponding quantum Fisher information matrices, and find that they can be fully expressed in terms of the mean displacement and covariance matrix of the Gaussian state. Finally, we give some examples to show the utility of our analytical results.