Theoretical Study On The Generation Of Entanglement And Quantum Computing

Recently, quantum information science has attracted much attention. As a new cross subject of information science and quantum mechanics, quantum information enriches the research fields of quantum mechanics and greatly promotes the development of quantum the-ory. In addition, the progresses in quantum information theory bring us the exciting future for science and technology. In quantum information science, the generation of quantum en-tangled states and quantum computation are two important subjects. The study of both quantum entanglement and its application are necessary and valuable not only to compre-hend the special properties of quantum mechanics but also to exploit the new information processing methods. Although quantum computation is still in its infancy, it is still difficult to implement multi-qubit quantum operation in experiments. Many national government and military funding agencies support quantum computing research for civilian and nation security purpose, and scientists have obtained some important results. The theoretical study on the generation of entangled state and quantum computation in the system of cavity QED are mainly discussed in this thesis. The thesis has been divided into seven chapters, with our own research works contained in the chapters from 3 to 7.In Chapter 1, the background and the position of the study are introduced, as well as the general situation of quantum entanglement is briefly described, and the organization of the dissertation is given at the end of this chapter.In Chapter 2, the basic concepts and theories in quantum information are introduced. Quantum bits, pure and mixed states, fidelity, quantum entanglement, and entanglement measurement methods are first introduced, then quantum gate operations, quantum comput-ing, quantum master equation, cavity QED system, and linear optics elements are reviewed.In Chapter 3, a protocol is proposed to implement nongeometric phase gates and generate entangled states by the adiabatic evolution of dark states in two distant cavities. The influence of various decoherence processes such as spontaneous emission and photon loss on the fidelity and success probability is also discussed using the quantum jump method. This protocol can be generalized to generate N-atom entangled states. An important advantage of the proposed protocol is that the interaction time of the atom and cavity need not to be accurately adjusted. In Chapter 4, the generation of a maximally four-dimensional entangled state of two six-level atoms is investigated in two remote cavities. Through choosing suitable intensities and detunings of fields, the atomic spontaneous radiation and photon leakage out of cavity and fibre can be efficiently suppressed. Thus, the intended state can be generated with high fidelity in the presence of decoherence. The scheme is extended to generate an N-atom four-dimensional entangled state. In addition, a system consisting of two multi-level atoms is also studied, which are trapped in two spatially separated cavities. Through appropriate choosing the parameters of the system, an effective long-range dipole-dipole interaction between the atoms is achieved. Based on the model, an arbitrary-dimensional entangled atomic state can be deterministically generated. Applying the method of master equation, the influence of photon decay and atomic spontaneous emission on the generation of atomic entangled state is also discussed.In Chapter 5, a scheme to implement the analog Grover search algorithm is proposed in a quantum network. Any atom with different marks can be found by adjusting the clas-sical fields according to the search condition. Moreover, the scheme can be generalized to implement the search process in the system consisting of more than three cavities. We show that the condition for the adiabatic approximation can be satisfied in the search process. In addition. the present scheme satisfies the Grover speedup approximately in a quantum network.In Chapter 6, the generation of GHZ and cluster states of three atoms is studied in a two-mode cavity. The advantages of the schemes are their robustness against decoherence due to the spontaneous emission of the excited states and the decay of the cavity modes. Moreover, the schemes can be generalized to generate N-atom entangled states. In this chapter. a method is also proposed to generate N-qubit cluster state by adiabatic passage in coupled cavities. The required interaction time remains unchanged with the increasing of the number of qubits and need not be accurately controlled. In addition, the scheme is robust against the fluctuations of some experimental parameters.In Chapter 7, firstly, generating W states by using single-photon interference and time-bin encoding in polarization noise channels is proposed. The polarization noise cannot affect the fidelity of the intended entangled state generation, and the successful probability does not change as the number of atoms in a single quantum node increases. In addition, implementing quantum swap gate and Fredkin gate encoded by atomic qubits are also investigated through the input-output process of the cavity. Through numerical calculations, the fidelity and photon loss probability for implementing the quantum swap gate between photon and atom are also discussed.Finally, the results are summarized and some problems for future research work are outlined.