Research On Quantum Decoherence And Entanglement Dynamics

Quantum information and quantum computation (QIQC). a new interdisciplinary field which involves quantum mechanics and modern information science, attracts much attention internationally from physicists both in theory and experiments, and much progress has been achieved. As one of the main goals of QIQC, quantum computer has more powerful ability to perform computation and information processing than its classical analog because of using quantum parallel algorithm which are designed by employing quantum coherence. However, due to decoherence, quantum coherence in QIQC will decrease, even vanish. Quantum decoherence is a main obstacle for quantum processors to realize quantum information processing. How to prevent decoherence is an interesting problem and one significant method to prevent quantum decoherence is to find decoherence-free subspaces in which quantum states don't perceive the presence of decoherence and can be used to design noiseless quantum code.Quantum entanglement attracts much attention from many researchers due to the fact that it plays an important role in QIQC as a valuable resource. Investigation concerning quantum entanglement is wide from its basic definitions to applications to experiments. As an interesting problem, quantum entanglement dynamics mainly refers to the time evolution of quantum entanglement. Research into quantum entanglement dynamics will be helpful for getting a clear knowledge of kinematic behavior of quantum entanglement in order to offer support for application of entanglement into QIQC exactly. In real world, the existence of decoherence will lead to coherence loss of quantum states, and the entanglement of quantum states will vary with time correspondingly.Quantum deochernece and quantum entanglement dynamics are correlated with each other. The change of quantum coherence due to decoherence will lead to variation of quantum entanglement. As one of few exactly solved models, Ising model is often employed to study decoherence because it has some physical instances. In chap. 2, we systematically investigate decoherence and entanglement dynamics of a generic quantum system under deeolierence induced by a pin environment consisting of a, transverse Ising model. Decoherence-free subspaces of the model under consideration have been found out. We find that quantum coherence loss and the time evolution of quantum entanglement depend not only on the temperature of environment and the coupling strength, but also on the size of quantum system and the initial states. Our results will contribute to a theoretical evidence to design noiseless quantum code and also a clear understanding of the effect of decoherence on quantum entanglement. As the second part of our research, the effect of stochastic dephasing on quantum coherence and quantum entanglement has been analyzed, and we find that quantum entanglement relies on the fluctuation of random variable in stochastic process. Our results imply that there is no decoherence-free quantum entangled state during stochastic process. As one complementary work along the line, the effect of stochastic dephasing on geometric phases is investigated by us, and the dependence of the correction of geometric phases on the variable of stochastic process and the frequency of system has been obtained qualitatively.This thesis consists of four parts. In chapter 1. we review the advance of quantum decoherence and introduce the basic definitions of quantum entanglement as well as related concepts. In chapter 2, a systematical analysis of quantum decoherence and quantum entanglement is made. In chapter 3, we investigate the effect of stochastic dephasing on quantum entanglement and geometric phases. In chapter 4, a brief summary of our thesis is given.