Quantum parameter estimation using general single-mode Gaussian states

TL;DR

This paper derives the quantum Cramér-Rao bound for parameter estimation using general single-mode Gaussian states, including mixed states, and provides a comprehensive solution for optimal measurement sensitivities.

Contribution

It unifies and completes the calculation of the quantum Fisher information for single-mode Gaussian states, covering multiple parameters and mixed states.

Findings

Derived the quantum Cramér-Rao bound for various parameters.

Provided the quantum Fisher information matrix for simultaneous measurements.

Unified previous partial results into a comprehensive framework.

Abstract

We calculate the quantum Cram\'er--Rao bound for the sensitivity with which one or several parameters, encoded in a general single-mode Gaussian state, can be estimated. This includes in particular the interesting case of mixed Gaussian states. We apply the formula to the problems of estimating phase, purity, loss, amplitude, and squeezing. In the case of the simultaneous measurement of several parameters, we provide the full quantum Fisher information matrix. Our results unify previously known partial results, and constitute a complete solution to the problem of knowing the best possible sensitivity of measurements based on a single-mode Gaussian state.