Asymmetric cloning in quantum information theory. – (Denis Rochette / LPT / Thèses). – 11/07/23, 16H

Soutenance de thèse

Denis Rochette, LPT, Salle de Conférence FERMI 3R4

Summary
This thesis studies quantum cloning and related quantum entanglement problems using fundamental concepts of representation theory, in particular those associated with the symmetric group. The research explores Schur-Weyl duality and its extensions, which allow efficient representation and manipulation of quantum systems, providing a valuable tool for quantum information theory. A main application of Schur-Weyl duality is the quantum cloning problem, which is studied both for cases 1 → 2 and for the more general cases 1 → N, providing new insights into the constraints imposed by the no-cloning theorem. The study is then extended to a more general quantum entanglement problem on a complete graph. The thesis is organised into chapters on Schur-Weyl duality, the mathematical foundations of quantum mechanics, quantum cloning problems and quantum entanglement problems, with an appendix providing an overview of representation theory.