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The defence will be in English.
Abstract: Quantum mechanics allows processes to be superposed, leading to a genuinely quantum lack of causal structure. This thesis examines causal indefiniteness via the process matrix formalism, which models processes with different parties that locally abide by the laws of quantum mechanics, without assuming a global well-defined causal structure, which leads to processes with so-called indefinite causal order. An example of such a process is the quantum switch, where the operations of two parties A and B are applied in a quantum superposition of the two possible orders, A before B and B before A. The main objective of this work is to provide a better understanding of processes with indefinite causal order for which a clear physical interpretation exists, both from a practical point of view by asking how they can be realised and what kind of new information processing advantages they can bring, but also from a more fundamental point of view, by looking at new properties that appear when considering processes with three or more parties, such as the so-called dynamical causal order. We study more formally the notion of dynamical causal order, which arises when the causal order is not fixed a priori but is instead established on the fly, with for instance the causal order between future parties depending on some choice of parties in the past. On top of a better understanding of causal indefiniteness, both at the fundamental and practical levels, this thesis includes a more personal part, that expresses my own reflections on the political and societal impact of scientific research, in the context of the development of quantum technologies.
