Study Of Quantum Entanglement、geometric Phase And Quantum Correlation In Dissipative Two-qubit System

Quantum entanglement, quantum correlation and quantum geometric phase have been hot topic in the studies of quantum information. We investigate a dynamics about them for two-qubit dissipative system by using the theories of quantum entanglement, quantum correlation and quantum geometric phase. Our work obtains some new results in the quantum information. The main innovation points are as follows:In the first chapter, we discuss the basic theories of quantum entanglement, quantum correlation including the conceptions and degree of entanglement and quantum discord.In the second chapter, we investigate the basic theories of quantum geometric phase including Berry phase, Pancharatnam phase and Aharonov-Anandan phase.In the third chapter, we study respectively the dynamic behaviors of two-qubit entanglement in various different environments, i.e., without environment dissipation, amplitude damping, phase damping, and the environment dissipation of amplitude damping with phase damping. The Pancharatnam phaseis also studied. The results show as follow:1. Under the situation without environment dissipation,We find that the dynamic behaviors and the phenomenon of entanglement death of two-qubit entanglement depends on initial phase angle. For the initial angle θ=π/4, the phenomena of death and revival are emerged. By choosing an initial angle, one can avoid such entanglement death.2.Under the situation of the amplitude damping dissipation, quantum entanglement decays smoothly in terms of exponent function for no dipole-dipole interaction,which the sudden death is not taken place. With the dipole-dipole interaction, the entanglement dynamics of two-qubit system oscillates cyclically and decays exponentially at the same time. It is obvious that the dipole-dipole interaction is a physical reason to lead to the cyclic oscillation. When θ=π/2, quantum entanglement would emerge the cyclic death and revival before the quantum entanglement becomes fully death. It is noted that one can avoid such entanglement death by using an adapt initial angle.3. Under the situation of the dephase damping, quantum entanglement would be sudden death with no dipole-dipole interaction. Under case of dipole-dipole interaction, quantum entanglement appears death and revival for the initial angle θ=π/2, When the initial angle θ=π/4, the cyclic evolution of concurrence disappears and the sudden death of quantum entanglement is taken place.4. The environment dissipation of amplitude damping with phase damping is similar to the dephasing one. The stronger the dissipation of its environment is, the faster the concurrence decays. 5. When the depahsing rate is equal to dipole-dipole interaction, the entanglement dynamics does not depend on initial phase angle and the phenomena of death and revival does not occour.The above results show:By controlling the coupling way between the two-qubit system and different environment, thus, we can avoid the sudden death of quantum entanglement.6. We study the Pancharatnam phase under the environment dissipation of amplitude damping with phase damping.The results show that the dissipative effect of open system affect the amplitude of the Pancharatnam phase, the Pancharatnam phase does not decay exponently. Compared with the dynamics of entanglement, Even though the quantum entanglement is death, the Pancharatnam phase is kept to evolve cyclically at all time. It is shown that the Pancharatnam phase has better feature of resisting decoherence and being robust.In the fourth chapter, we investigate the dynamic behavior of quantum correlation under both two-side and one-side decoherence with multi-mode squeezed vacuum field. The dynamic behavior of the concurrence and quantum discord is studied with the influence of the squeezing parameter r of multi-mode squeezed vacuum field and the dipole-dipole interaction1. under the both-side dissipative environment, the dynamic behaviors of concurrence, quantum discord and classical correlation present different attenuation. In the absence of dipole-dipole interaction, the classical correlation is greater than the concreence in the early stage of the evolution, quantum discord is smallest. After short time evolution, concurrence appears the phenomenon of sudden death.With an increasing of squeezed parameter, i.e., an average photon number, the entanglement time of two-qubit system becomes short so that the death of entanglement is early taken place,but quantum discord and classical correlation decay more slowly to death. The dynamic behaviors of quantum discord and concurrence present decaying with periodic oscillation for dipole-dipole interaction, and quantum discord present the phenomenon of periodical attenuation and enhancing but no sudden death. The oscillation cycle depend on the intensity of dipole-dipole interaction.The phenomena of death and revival occours to concurrence and the time of sudden death takes place early for increasing of intensity of dipole-dipole interaction2.The dynamic behavior of quantum discord、concurrence and classical correlation for the one-side dissipation is similar to the one for the two-side dissipation. Under the same initial conditions, however, the decay speed of the quantum discord、concurrence and classical correlation for the one-side dissipation is slower than for the two-side dissipation. In the fifth chapter, the conclusions and discussions of the thesis and the outlook of this topic are given for the geometric quantum computation.