| Quantum information and quantum computing are the hot topics of current physical studies and the rising interdisciplinary fields procreated through the combination of quantum theory with classical information science. Quantum entanglement is a key resource in realizing quantum information and quantum computing and also the ultimate factor for this field exhibiting great advantage and application foreground. By means of quantum entanglement one can achieve some tasks which can not be realized via classical methods, such as quantum teleportation, quantum dense coding and quantum cryptography and so on. Multipartite entangled state has more abundant structures and more complex properties, which would have more extensive applications in quantum information processing. However, in the process of system distribution as well as particle manipulation, each particle would unavoidably interact with uncontrollable external environment and this local decoherence would eventually destroy the necessary entanglement of the whole system. Therefore, the study of entanglement dynamics in various models, particularly the entanglement dynamics of multipartite system, not only have great theoretical interests in understanding the concept of quantum entanglement but also have potential application values in quantum information processing and quantum computing. The main results of this thesis are as follows.1. We studied the conditions of atomic finite-time disentanglement in cavity QED. The finite-time disentanglement, which is also termed as entanglement sudden death (ESD), refer to the entanglement of a composite system can decay to zero in a finite time, exhibiting clear difference to the exponential decay of the coherence of a single quantum system. The finite-time disappearance of entanglement put a limitation on its practical application and attracted extensive attentions. In this work, through three different physical models, we investigated the conditions which can induce atomic ESD in cavity QED. The results show that the photon numbers in cavity and the purity of atomic initial entanglement have direct influences on the occurrence of ESD. The results simultaneously indicate the methods to control ESD. The work offer valuable references for further studies of the reason of ESD as well as the control scheme for it.2. We studied the entanglement robustness of multiqubit entanglement in local decoherence. We investigated the entanglement dynamics of a generalized N-qubit asymmetric Greenberger-Horne-Zeilinger (GHZ) type entangled state in local decoherence. The results show that this asymmetric GHZ type state is more robust than its symmetrical counterpart in resisting the decoherence of environment. The previous studies shown that the symmetrical GHZ type state can decay to zero in finite time, namely, exhibiting the phenomenon of ESD. Nevertheless, we further show that the asymmetric GHZ type state does not suffer from ESD in all the possible parameter domains. Due to the possible transform of the two states via local unitary operation, we conclude that local operation can enhance the entanglement robustness in realistic environment. This conclusion exhibits clear contrast with the previous understanding of local unitary operation, that is, local operation can not change the entanglement degree. Therefore, it is a valuable complement to the previous conclusion. At the same time, our results have explicit application values in the sense that it not only provides a good reference for the choice of more robust type of entanglement in practical quantum information processing and quantum computing, but also provides an efficient method to change the less robust entanglement to the more robust one.3. The entanglement dynamics of a six-qubit model in cavity QED is studied. The model consists of three two-level atoms which are prepared initially in GHZ-type or W-type entangled state and coupled with three spatially separate cavity field. The three independent atom-cavity subsystems have no any interactions and they can only transfer information through entanglement. We explored two classes of GHZ-type and two classes of W-type states. The states belong to the same class of entanglement are distinguished from different initial excited state populations. The results show that for both two classes of GHZ-type and W-type states, only one class that has more excited state population can experience ESD. We also studied the entanglement creation of the corresponding cavity fields. Since the three cavites are independent, the entanglement creation between them indicate the transfer of entanglement from atomic subsystem to the cavities'subsystem.4. Motivated by certain practical quantum information processing, we designed and studied the entanglement dynamics for a double TC model. We proposed an interaction strength theory to explain the appearing condition and parameter domain for ESD. The double TC model comprises four two-level atoms A, B,C,D and two spatially separate single-mode cavities a, b. In the beginning, atom-pairs AB and CD are prepared in bipartite entangled state, while the two cavities are prepared in the vacuum state, non-zero photon number state and general thermal state, respectively. The independent atoms A,C (B,D) that belong to different entangled atom-pairs are embedded in one and the same cavity a (b), and interact with it via TC interaction. We investigated in detail the dynamical characters of entanglement in various conditions of cavity fields and different initial state of atoms. We also compared the results with that in double JC model. These results appeared in the double TC and JC model (i.e., the domains of ESD) can be explained by means of our proposed interaction strength theory. According to the theory, ESD can happen in strong regime of system-environment interaction while does not in the weak one.5. We presented a simple entanglement measure for multiqubit system. The advantage of our entanglement measure is that it can detect the global separation of multiqubit system, that is, its value reaches exactly zero when the total system is completely separate. We established the generalized entanglement monogamy relations for multiqubit system and the associated partition-dependent residual entanglement measure for genuine multipartite entanglement. By means of these quantities, we studied the entanglement dynamics of N-qubit GHZ-type and W-type states in both Markovian and non-Markovian environments. We demonstrated in detail the transition of bipartite and multipartite entanglement. We studied the memory effect of non-Markovian environment on the entanglement recovery after vanishing and found also the distinct dynamical behaviors of GHZ-type and W-type states. These studies would shed some light on the understanding of multipartite entanglement from points of both mathematics and dynamics views.
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