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 applies it to various estimation problems, providing a comprehensive solution.

Contribution

It provides a complete formula for the quantum Cramér-Rao bound for all parameters encoded in single-mode Gaussian states, unifying previous partial results.

Findings

Derived the quantum Cramér-Rao bound for mixed Gaussian states.

Applied the bound to estimate phase, purity, loss, amplitude, and squeezing.

Provided the quantum Fisher information matrix for simultaneous multi-parameter estimation.

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.