Entanglement and generalized bell inequalities

Abstract

Violation of Bell inequalities is one way to test entanglement which is a valuable resource in quantum information theory. The overall objective of this thesis is to develop Bell inequalities for multipartite systems of higher dimensions and explore their applications. To achieve this overall objective, different types of systems: N qubits, 2 quNits, and 3 quNits are investigated. For N qubits, we examine quantum entanglement of quantum systems with both discrete variables and continuous variables through their violation of the Zukowski-Brukner inequalities. For 2 quNits, new Bell inequalities in terms of correlation functions are constructed. Entanglement of bipartite quantum systems of arbitrary dimensions with continuous variables is examined by violating the inequalities. In addition, maximal violation of the CGLMP inequalities is investigated in order to find its limit and the states which maximally violate the inequalities. New Bell inequalities involving both probabilities and correlation functions for 3 qubits are found so that Gisin's theorem can indeed be generalized to 3 qubits. A new Bell inequality for tripartite systems of four dimensions is also formulated. In addition, an experimental setup for testing violation of local realism by using 3-qubit Bell inequalities is proposed.