Entanglement Evolution In Multipartite Quantum Systems

Quantum information and quantum computation is a advance topic in the scientificresearch at present. It is a burgeoning interdiscipline and of quantum mechanic andclassical information science. Quantum entanglement has been regarded as a keyresource for quantum information processing and quantum computing. It is fundamentalproblem that the new interdiscipline exhibits the striking advantage and broadapplications. By utilizing quantum entanglement, there are some tasks can beaccomplished, such as quantum teleportation, quantum dense coding, quantumcryptography based on the entangled states and so on which can not be done by classicalmethod. The structure of multipartite quantum entanglement is more complicated thanthat of bipartite entanglement, which can be used in the practical quantum informationprocessing. However, in the procedure of quantum system distribution and the quantummanipulation, the quantum system always interacts with the environment. The induceddecoherence can destroy the quantum entanglement in the system which is the crucialresource in the quantum information processing. Hence, the study on the entanglementevolution under different environment models is a basic problem in quantum informationprocessing. In particular, the characterization of entanglement evolution in multipartitequantum systems is useful for the understanding of quantum entanglement concept whichhas not only the theoretical significance but also the practical application for the quantuminformation processing and quantum computation.In the evolution of quantum entanglement, the quantification of quantumentanglement is very important. In this case, a computable entanglement measure isdesirable. Up to now, there are a lot of results on the qualitative and quantitativecharacterization for quantum entanglement, especially in the bipartite case. However, tillnow, there is not a generic entanglement measure for multipartite quantum systems.Nowadays, for the two party and low-dimensional quantum system, there are somecomputable entanglement measures. While for tripartite quantum systems, there is a little knowledge about the entanglement characterization. Only for the bipartite quantumsystem, there are maximal entangled states and one can obtain the entanglement value incomparison to the maximal entangled state’s entanglement. But, there is no similarmaximal entangled state in the multipartite entangled quantum system. So, we have nomethod to extend directly the biparitite entanglement measure to the multipartite case. Atpresent, there are only a little knowledge about the multipartite quantum entanglement,even the qualitative understanding about the multipartite entanglement is finite. In thequantum information processing, it is necessary to study the entanglement property ofmultipartite quantum system. Meanwhile, there are more properties in the multipartiteentanglement compared with that of bipartite entanglement. It is deserved to study theentanglement evolution in multipartite system which has broad applications in thequantum information processing. In summary, the study on the entanglement evolution inthe multipartite quantum system has both theoretical and practical meaning, which is thereason why we choose the problem in this thesis.This dissertation is mainly focused on the entanglement evolution in multipartitequantum systems. The dissertation is organized as follows.In Sec. I, some background knowledge about quantum information and quantumcomputation is introduced, by giving some basic concept, such as quantum state,entangled state, entanglement measure and so on. In Sec. II, we give an introductionabout the full quantum theory on the interaction between atom and radiation field. Wealso give the description on theoretical model used in this dissertation. In Sec. III, Westudy the entanglement evolution of a three-qubit mixed state in the multipartitecavity-reservoir system. We study the entanglement evolution of a mixed state composedof a GHZ and a W state via the negativity, a computable entanglement measure. We getthe following results.Firstly， for a composite system consisting of three cavities interacting withindependent reservoirs, it is shown that the entanglement evolution is restricted by a setof monogamy relations. Furthermore, as quantified by the negativity, the entanglementdynamical property of the mixed entangled state of cavity photons is investigated. Secondly, it is found that the three cavity photons can exhibit the phenomenon ofentanglement sudden death (ESD). However, compared with the evolution of ageneralized three-qubit GHZ state which has the equal initial entanglement, the ESDtime of mixed states is latter than that of the pure state. Finally, we discuss theentanglement distribution in the multipartite system, and point out the intrinsic relationbetween the ESD of cavity photons and the entanglement sudden birth of reservoirs.The study on the entanglement evolution of three cavity photons is helpful for adeep understanding on the entanglement evolution of the multipartite quantum system.And at the same time, it gives some indications in manipulating the entanglementexperimentally. The composite system in this thesis can be generalized to other casewhich need to be studied in future.