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Contributions relatives à la génération quantique d’aléa

Abstract : The deterministic nature of classical physics does not allow true randomness production. Quantum physics, on the other side, makes probabilistic forecasts about processes that seem to be intrinsically random. Moreover, answers to EPR type paradoxes, like the answer formulated through Bell inequalities [16], show that quantum physics can not be completed in a full deterministic theory. We may wonder what are the quantum ex-periments allowing true randomness production. Cristian S. Calude and Al [4] show that almost all quantum measurements produce genuine randomness (Strong Kochen Specker theorem and its consequences). In our works, we aim to produce randomness using this latter result. Our schemes (see [10,13]) use products of incompatible observables implemented one after the other like in [36]. To improve the security of this protocols, we deduce, new quantum inequalities from existing inequalities namely CHSH [28] and CHSH-3 (initially CGLMP forqutrits [29]). Here, we consider configurations using only one qutrit, where the constrain of commuting observables is released. The classical bounds are then obtained under the hypothesis of macroscopic reality defined in [51] (and also used for classical bounds of temporal inequalities [36]). This classical bounds are the same as in the frame of local realism. However, the quantum bounds, obtained by SDP, can be greater than those of the original expressions, allowing thus a better resistance to noise and attacks. This violations with respect to classical bound are no more due to non locality but, to indefiniteness of outcomes of quantum measurements. The optimum states and measurements of this inequalities allow us to give self testing arguments for our protocols. During this PhD, we also give an analysis of some aspect of quantum cryptography as QKD.
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Don Akou Jean Baptiste Anoman. Contributions relatives à la génération quantique d’aléa. Théorie des nombres [math.NT]. Université de Limoges, 2021. Français. ⟨NNT : 2021LIMO0097⟩. ⟨tel-03548917⟩

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