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.Comment: PhD Thesis, 173 pages, 15 figures, keywords: quantum metrology,
Gaussian states, quantum field theory, quantum reference frame
