Abstract:
In this thesis we have studied a quantum phenomenon called quantum entanglement in different contexts. The mathematical formalism of paraquantum theory has been used to derive the even and odd paraquantum coherent states. We have used the concurrence to measure the bipartite entanglement of paraquantum coherent state. The behavior of the concurrence in function of the paraquantization parameter c and the coherence parameter � has been studied and analyzed. It is shown that the paraquantisation has an inverse relation with the bipartite quantum entanglement. In the second context we have studied the quantum entanglement in noncommutative Bianchi I space-time. In the first step, we have studied the pair creation mechanism. First of all, we have derived the noncommutative Dirac equation and differentiate between positive and negative modes. Then, we have calculated the fermions-antifermions pair creation density using the Bogoliubov coefficients. To measure the modes entanglement we have
used the Von Neumann entropy S!.! .
The behavior of S!.! in function of noncommutativity θ parameter and k!-modes frequencies has been presented. It is shown that the noncommutativity plays an important role and it has a direct effect on quantum entanglement, such that in a region it plays the role of gravity and in another region it behaves like a repulsive force. The results and discussions of variations of S!.! with respect to the behaviors of noncommutativity have been presented.
