Quantum physics has led to a revolution in our conception of the nature of our world and is now bringing about a technological revolution. The use of quantum information promises indeed applications that outperform those of today’s so-called classical devices. Continuous variable quantum information theory refers to the study of quantum information encoded in continuous degrees of freedom of quantum systems. This theory extends the mathematical study of quantum information to quantum states in Hilbert spaces of infinite dimension. It offers different perspectives compared to discrete variable quantum information theory and is particularly suitable for the description of quantum states of light. Quantum optics is thus a natural experimental platform for developing quantum applications in continuous variable. This thesis focuses on three main questions: 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? These three questions are at the heart of the development of future quantum technologies and we provide several answers within the frameworks of continuous variable quantum information and linear quantum optics.

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Continuous variable quantum advantages and applications in quantum optics

Quantum physics has led to a revolution in our conception of the nature of our world and is now bringing about a technological revolution. The use of quantum information promises indeed applications that outperform those of today’s so-called classical devices. Continuous variable quantum information theory refers to the study of quantum information encoded in continuous degrees of freedom of quantum systems. This theory extends the mathematical study of quantum information to quantum states in Hilbert spaces of infinite dimension. It offers different perspectives compared to discrete variable quantum information theory and is particularly suitable for the description of quantum states of light. Quantum optics is thus a natural experimental platform for developing quantum applications in continuous variable. This thesis focuses on three main questions: 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? These three questions are at the heart of the development of future quantum technologies and we provide several answers within the frameworks of continuous variable quantum information and linear quantum optics.