Continuous variable quantum advantages and applications in quantum optics

Summary Quantum physics has brought a conceptual revolution as to the nature of our world and today brings a technological revolution. Indeed, the use of quantum information promises applications that surpass the current so-called classical machines. The theory of quantum information in continuous variables is the study of the possibilities offered by the encoding of information in continuous degrees of freedom of quantum systems. Mathematically, this theory extends the study of quantum information to quantum states in infinite dimensional Hilbert spaces. It offers different perspectives from quantum information in discrete variables and is notably adapted to the description of quantum states of light. Quantum optics is thus a natural experimental platform to develop quantum applications in continuous variable. The thesis focuses on three main questions: Where does the quantum advantage come from, i.e. the ability of quantum machines to outperform classical machines? How can we ensure the proper functioning of a quantum machine? What advantages can be gained from the use of quantum information? These three questions are at the heart of the development of quantum technologies, and we provide several answers in the framework of continuous variable quantum information theory and linear quantum optics.