| Quantum information and quantum computation, an interdisciplinary field which involves quantum mechanics, computer science and the theory of information, has attracted more and more interests. It is significant in both foundational science and application. It does not only enhance the understanding of the quantum theory, but also impact the field of national defense and commerce. For example, absolutely secure quantum cryptogram system have been established base on the quantum no-cloning theorem which said that the quantum information can't be copied as classical information. And, parallel quantum algorithm base on the quantum coherence, have been used to solve the hard problems for the classical computer, like the factorization of large numbers.Many quantum system have been proposed in the quantum information processing (QIP), like cavity QED, ion trap, quantum dot, and NMR. Applied quantum information processing should been realized in systems that easy to be extended and integrated. Spin system is such a solid system, it has been proposed to been used in quantum information storing and quantum memories, quantum computation, quantum clone, and quantum state transfer and so on. Quantum entanglement is important resource in quantum information science, so the study on the entanglement in the spin system will be helpful to the practical application. It is also the main point of this thesis.Firstly, we discuss the thermal entanglement in spin chain. A physically realizable quantum mechanisms are not always at zero temperature but often in a thermal equilibrium, so the study on the entanglement in thermal state is very important for the quantum information science. We choose the XXZ model to investigate the pairwise thermal entanglement in spin chain. The effects of spin, number of sites, anisotropic parameter, and magnetic field on the threshold temperature are discussed respectively. We find that: (l)The threshold temperature decreases with the increasing of the number of sites and finally trends to be a constant. (2)With the increasing of spin, threshold temperature inereases almost linearly and becomes sufficiently high, imply that the larger spin systems like molecular magnets should be better in the QIP with high temperature. (3)The effect of anisotropic parameter is observable, with the increasing of anisotropic parameter, threshold temperature decreases and vanishes at a point nearâ–³= 1. (4) The external magnetic field can also influence the entanglement but not change the threshold temperature.For the further study on the thermal effect in the QIP, we discuss the quantum state transfer through a thermal spin chain, the quantum state is transmitted from one end of the chain to the other end. We find that the maximal fidelity does not decrease monotonously with the increasing of the temperature, but depends on the maximal allowed transfer time. We also compare the results of thermal channel with the transfer through ground state channel, and find that the thermal channel is sometimes better than the ground state channel. This results mean that, the thermal noise influences but does not destroy the quantum state transfer vitally, the transfer does not need to be processed in extreme low temperature.Finally, We study the dynamic evolution of the entanglement in the spin channel with an XY-type interaction initially in an entangled state. We find that the phenomenon of entanglement sudden death (ESD) appears in the evolution of entanglement for some initial states. We calculate the entanglement and obtain the parameter regions of disentanglement for the chains with several numbers of sites. The influence of environment is also discussed, we find that the present of environment will speedup the decoherence and enlarge the regions of disentanglement. These results are helpful to apply or avoid the ESD in the QIP. Further more, we can use an additional external field to modulate the evolution of the entanglement, change the regions of disentanglement as needed, that is our research topic next stage. |
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