Nonlocality of symmetric states and its applications in quantum information. (Non-localité des états symétriques et ses applications en informatique quantique)

This thesis is about the nonlocal properties of permuation symmetric states and the potential usefulness of such properties in quantum information processing. The nonlocality of almost all symmetric states, except Dicke states is shown by constructing an $n$-party Hardy paradox. With the help of the Majorana representation, suitable measurement settings can be chosen for these symmetric states which satisfy the paradox. An extended CH inequality can be derived from the probabilistic conditions of the paradox. The inequality is shown to be violated by all symmetric states. The nonlocality properties and entanglement properties of symmetric states are also discussed and compared, natbly with respect to persistency and monogamy. It is shown that te degeneracy of some symmetric states is linked to the persistency, which provides a way to use device independent tests to separte nonlocality classes. It is also shown that the inequalities used to show the nonlocality of all symmetric states are not strictly monogamous.A new inequality for Dicke states is shown to be monogamous when the number of parties goes to infinity. But all these inequalites can not detect genuine nonlocality. Applications of nonlocality to communication complexity and Bayesian game theory are also discussed.

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