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Normalité asymptotique locale quantique et autres questions de statistiques quantiques

Abstract : The thesis deals with miscellaneous quantum statistics problems, where the starting point is the object itself, instead of measurement data. We use model selection methods on quantum homodyne tomography. We apply our results to photocounter calibration. We study optimal discrimination of quantum states and Pauli channels, in a minimax setting. We devise an estimation scheme for unitary transformations, which has 1/n convergence speed. We give a sufficient condition for a measurement to be clean, as defined by Buscemi et al. , and characterise clean measurements on qubits. We prove there are not five complementary subalgebras isomorphic to M2(C) in M4(C). The main theme is strong quantum local asymptotic normality. We prove that i.i.d. experiments are asymptotically equivalent to quantum Gaussian shift experiments. Ln other words, many copies of a finite-dimensional system correspond to a single copy of a Gaussian state on a CCR-algebra of the right dimension, with mean as unknown parameter. This means that there are channels that transform one state into the other, and back, without knowing the precise state. Hence, all problems solved for quantum Gaussian shift experiments are asymptotically solved for i.i.d. experiments, ln particular, we give an explicit optimal estimation method for any well-behaved loss function, both in the minimax and Bayesian uniform frameworks.
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https://hal.inria.fr/tel-01657373
Contributor : Jonas Kahn <>
Submitted on : Wednesday, December 6, 2017 - 4:05:18 PM
Last modification on : Friday, November 27, 2020 - 11:16:03 PM

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Jonas Kahn. Normalité asymptotique locale quantique et autres questions de statistiques quantiques. Physique Quantique [quant-ph]. Université Paris XI, 2009. Français. ⟨tel-01657373⟩

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