Gaussian quantum metrology and space-time probes

TL;DR

This thesis advances Gaussian quantum metrology by deriving new optimal estimation formulas, analyzing the effects of temperature and reference frames, and proposing methods for estimating space-time parameters with practical implications.

Contribution

It introduces new formulas for multi-parameter estimation in Gaussian states and develops a practical method for optimizing probe states in Gaussian channel estimation.

Findings

Temperature impacts estimation via four multiplicative factors

Squeezed thermal states have specific performance characteristics

Quantum reference frames can mitigate estimation issues without shared references

Abstract

In this thesis we focus on Gaussian quantum metrology in the phase-space formalism and its applications in quantum sensing and the estimation of space-time parameters. We derive new formulae for the optimal estimation of multiple parameters encoded into Gaussian states. We discuss the discontinuous behavior of the figure of merit - the quantum Fisher information. Using derived expressions we devise a practical method of finding optimal probe states for the estimation of Gaussian channels and we illustrate this method on several examples. We show that the temperature of a probe state affects the estimation generically and always appears in the form of four multiplicative factors. We also discuss how well squeezed thermal states perform in the estimation of space-time parameters. Finally we study how the estimation precision changes when two parties exchanging a quantum state with the encoded parameter do not share a reference frame. We show that using a quantum reference frame could counter this effect.