The Applications Of Quantum Algebra In Quantum Information

In this thesis, by making use of Yangian algebra, we mainly study quantum entanglement, quantum fidelity and quantum teleportation in quantum information theory. We mainly focus on the experimental operability of our models in order to find the relations between the experiment and theory.In light of the transition property of Yangian generators, we study the effects of Y(sl(2)) algebra on the entangled degree of the pure state in two-qubit system. Through constraint condition, we obtain the reduced Yangian Y(sl(2)). Our results show that the concurrence can be reduced to zero by the reduced Yangian operators. However, this situation can not be achieved for the generic Yangian operators. In two qubits XY model, we study the energy level crossings of the ground state and the evolution of the fidelity between thermodynamics equilibrium state of system and the ground state. We find that the fidelity is very sensitive to the anisotropic factor of the magnetic field. By making use of the transition of Y(sl(2)), our results show that the high fidelity represents sudden death in a quadrant, then sudden birth in another one in the magnetic field plane. These results indicate that magnetic field factor and Yangian operators may be used as a controller of fidelity.In the two-qubit Heisenberg XY model, different parameter values of the transition operators lead to different evolutions of the entanglement degree of the final states. It is interesting that our results have a certain connection with the experimental result by taking some special parametric values. We propose the relation between Yangian and the experiment. Regulating the coupling capacitance, inductance and voltage in experiment are equivalent to adjusting Yangian coeffcients in theory for changing the concurrence of system.In addition, we promote the effects of Y(sl(2)) algebra on entanglement to Y(su(3)) algebra. Then every generator of the general and reduced Yangian Y (su(3)) is applied to the mixed light pseudoscalar meson state. We find that the general generator can not make the initial states disentangled by acting them on the initial states. However, the reduced ones are able to make the initial state disentangled. In addition, we show the effects of every Y (su(3)) generator on the decay channel and find out possible the decay channels.For the controllable two-superconducting-qubit system coupled with a fixed capacitor in the experiment, we study and analyze the evolution of the thermal quantum entanglement versus the important physical parameters. Our results show that our theoretical result is in accordance with the experimental data and the entangled degree of the system is greatly enhanced in the case of very low temperature and Josephson energies for the identical superconducting qubits. Hence utilizing the results of calculation and investigation, we may generate better entangled and stable states by adjusting the experimental parameters, which can be realized experimentally by changing the capacitance and LC circuits.As a well-controlled object, quantum dot shows the wide application prospect. We study the thermal entanglement of the vertical quantum dot, and apply it to research quantum teleportation. We obtain the parametric conditions of high entangled degree and the expression of the critical temperature with disentanglement. By making use of the standard transport protocols and the Bell measurement bases, we investigate quantum teleportation with quantum dot as quantum channel. Our results show that the fidelity of teleportation is highly stable and quality.