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Theses

L'information quantique encodé en gravité semi-classique

Dongsheng Ge 1, 2
2 Champs, Gravitation et Cordes
LPENS (UMR_8023) - Laboratoire de physique de l'ENS - ENS Paris
Abstract : The holographic duality renders a way to encode certain quantum information in a semi-classical grav- ity theory. In this thesis, we start with the quantum complexity, considering the universality of its two holographic conjectures, “Complexity=Volume” (CV) and “Complexity=Action” (CA), in terms of the thin brane model in AdS₃. Our result shows that the divergence structures for the two are not identical, as CV has an extra brane tension dependent logarithmic divergence. Though preliminary considerations on the field theory side of complexity favor CA, the universality question is still kept open. Next we move to a study on the gate dependence of circuit complexity by explicit calculation in the two-dimensional bosonized model where we show that the influence of the gate set choice is different for different subsets of states under consideration, not significant for “bosonic coherent-fermionic gaussian” case, while dramatically different in the bi-gaussian case. Then, we reconsider the thin-brane model in the canonical holographic manner, finding that the brane tension is related to the energy transport coefficients defined in the dCFT, in addition to the relation to the boundary entropy of the interface which has been commonly advertised in the literature. In the last part, we propose a new bulk geometric quantity dual to the berry curvature in the space of boundary modular hamiltonians, which is the Riemann curvature in the vicinity of the Hubeny-Rangamani-Takayanagi surface. A sanity test has been done in pure AdS₃ which shows a nice agreement due to the simplicity and nice symmetries of this system.
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Dongsheng Ge. L'information quantique encodé en gravité semi-classique. Mathematical Physics [math-ph]. Université Paris sciences et lettres, 2020. English. ⟨NNT : 2020UPSLE015⟩. ⟨tel-03262512⟩

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