Quantum Entanglement And Quantum Computation In Solid-state Spin Systems

In this thesis, the entanglement properties of one-dimensional solid-state quantum spin systems are investigated. By means of some different entanglement witnesses, the conditions of the existence of thermal and ground-state entanglement are provided. From the origin of quantum entanglement, the quantum criticality of the ground state in many-body quantum systems is studied. Some typical solid-state quantum spin systems have been applied to the quantum information processing. Some feasible schemes of quantum computation are proposed. The effects of the realistic environment are taken into account.In the thesis, based on the definition of quantum entanglement, some efficient witnesses can be obtained by some measurable physical qualities. Through these entanglement witnesses, the entanglement properties of one-dimensional solid-state quantum spin chains are investigated. The spin chains include a spin-s Heisenberg chain, mixed-spin chain, and hardcore Boson-Hubbard chain. The critical temperatures for the existence of the thermal entanglement are given. When the physical temperatures of the systems are lower than the critical temperature, the corresponding thermal equilibrium states are entangled. With the increase of the temperatures, the thermal entanglement vanishes gradually. Compared with other theoretical measures, these entanglement witnesses based on measurable qualities can provide one necessary condition for the existence of the entanglement. The numerical calculation shows that the entanglement in rather low temperatures in the solid state systems with a great number of spins can be detected. For the many-body quantum systems, the multipartite and bipartite ground state entanglement is investigated. The relation of global entanglement and quantum phase transition is obtained. In the real solid state spin system, the multipartite entanglement vanishes more rapidly than bipartite entanglement. In regard to the impacts of the environment on the entanglement, the time evolution of a small number of atoms in the vacuum reservoir is analyzed by means of the master equation. If there is only one excited atom in the ensemble, a pair of atoms originally at the ground states can be entangled. The dynamical behavior of the entanglement is similar to the damped Rabi oscillation whose amplitude is tuned by the spontaneous decay. The exact solution of the quantum states can help for the understanding of the physical essence of the entanglement existence. It is seen that the entanglement is dependent mainly on the transition probability between the excited state of one atom and ground state of another one.In the thesis, some methods of solid spin-based quantum computation are proposed. The anisotropic and asymmetric exchange interactions are considered in the model which is close to the practical conditions. The conditions of the exact swap gate in the anisotropic Heisenberg XXZ model is presented by solving exactly the time evolution of single-qubit states. The effects of the quantum fluctuations in the systems are analyzed. The feasible experimental scheme is provided. Through the asymmetric interaction existing in the model of two coupled electron spins in semiconductor quantum dots and by means of single-qubit rotations, the two-qubit Controlled-NOT gate is constructed. The quantum computation with high accuracy can be implemented. In the experiments of solid-state quantum information processing using quantum spin system, the short distance of operations is regarded as one big obstacle. A scheme based on the quantum spin bus with two coupled chainsis proposed. When the bus is always frozen at the non-degenerate ground state, the effective long-range interaction can be obtained by the electrical control of the weak coupling between some qubits and the bus. Thus, a set of universal quantum logic gates can be set up to realize quantum computation in long distance.