The implementation of optical quantum technologies requires precise and complete characterisation
tools for multi-mode nonclassical states of light. In this thesis, we propose and
we implement experimentally three applications of optical quantum measurements, which
combine aspects of light that are described by both discrete and continuous variables.
In the rst part of this thesis, we present a new scheme for interferometric phase estimation,
which uses double homodyne measurements as an alternative to photon counting.
We show that, without requiring a phase reference, this scheme can achieve the optimum
phase estimation precision for all path-symmetric probe states with a de ned number of
photons. Furthermore, the estimation procedure is robust against state preparation imperfections,
and naturally yields the same precision for all values of the estimated phase. We
implement the proposed scheme experimentally, using a polarisation interferometer probed
by a single-photon signal, and temporally multiplexing a single homodyne detector. We
repeat the experiment with classical probe states. For both cases, we demonstrate the accuracy
and precision of the proposed method, our implementation deviating by 5% from the
fundamental precision bound. We demonstrate that, in our scheme, single-photon probe
states can provide better precision than weak coherent ones. These results indicate that
hybrid quantum resources, which combine tools from the discrete and continuous-variable
paradigms, can play a signi cant role in practical sensing scenarios.
In the second part of this thesis, we present an application in the eld of information
thermodynamics, reporting an experimental realisation, in a photonic setup, of Maxwell's
demon. We show that a measurement at the few-photons level, followed by a feed-forward
operation, allows the extraction of work from intense thermal light into an electric circuit.
The interpretation of the experiment leads us to the derivation of an equality relating work
extraction to information acquired by measurement. We prove a bound using this relation,
and show that it is in agreement with the experimental results. Our work puts forward
photonic systems as a platform for experiments in the eld of information thermodynamics.
In the third part of this thesis, we present a new method for the characterisation of
broadband parametric down-conversion, based on stimulated frequency generation. In particular,
we analyse the information contained in the frequency generation produced in the
same mode as a seeding beam, for a type-II down-conversion process. We derive a model
for this signal and argue that its detection can provide a useful characterisation tool in the
high-gain regime, allowing for a self-referenced estimation of squeezing gain. We propose
a method for measuring this signal and present an experimental realisation, based on a
wave-guided source, at telecommunication wavelengths. Our experimental results demonstrate
that the proposed measurement is an e ective experimental handle for discerning the
intricate structure of broadband parametric down-conversion.