  This thesis focuses on three main questions in the continuous variable and
optical settings: where does a quantum advantage, that is, the ability of
quantum machines to outperform classical machines, come from? How to ensure the
proper functioning of a quantum machine? What advantages can be gained in
practice from the use of quantum information?
  Quantum advantage in continuous variable comes in particular from the use of
so-called non-Gaussian quantum states. We introduce the stellar formalism to
characterize these states. We then study the transition from classically
simulable models to models which are universal for quantum computing. We show
that quantum computational supremacy, the dramatic speedup of quantum computers
over their classical counterparts, may be realised with non-Gaussian states and
Gaussian measurements.
  Quantum certification denotes the methods seeking to verify the correct
functioning of a quantum machine. We consider certification of quantum states
in continuous variable, introducing several protocols according to the
assumptions made on the tested state. We develop efficient methods for the
verification of a large class of multimode quantum states, including the output
states of the Boson Sampling model, enabling the experimental verification of
quantum supremacy with photonic quantum computing.
  We give several new examples of practical applications of quantum information
in linear quantum optics. Generalising the swap test, we highlight a connection
between the ability to distinguish two quantum states and the ability to
perform universal programmable quantum measurements, for which we give various
implementations in linear optics, based on the use of single photons or
coherent states. Finally, we obtain, thanks to linear optics, the first
implementation of a quantum protocol for weak coin flipping, a building block
for many cryptographic applications.
