Engtanglement And Fedility In Quantum Spin Systems

In this paper, we briefly introduce some fundamental theories in quantum information technology. These theories include quantum entanglement, quantum computations, and fidelities, etc. We propose some schemes of quantum teleportation and quantum computations using entanglement and review some methods of evaluating entanglement. We investigate in detail the properties of solid state quantum system——the Heisenberg spin chain system. The applications of Heisenberg spin chain in quantum information theory are discussed.In many real spin systems, there are complicate energy levels. These spin systems are usually modeled by spin-S (S>1/2) quantum systems. In view of practical applications, the entanglement in an anisotropic spin-1 Heisenberg chain with uniform magnetic field is investigated. The ground-state entanglement will undergo different kinds of transitions when the anisotropy coefficientΔand the amplitude of the magnetic field B are varied. The thermal entanglement of the nearest neighboring always declines when B is increased no matter what the value of the anisotropy is. It is very interesting to note that the entanglement of the next nearest neighboring can be increased to a maximum value at certain magnetic field. Regardless of the boundary conditions, the nearest neighboring entanglement is always decreased and approaches to a constant value when the size of the system is very large. The constant value of open boundary condition is much larger than that of periodic boundary condition.In the investigations of quantum teleportation, fidelity of the quantum channel is an important standard for evaluating its quality in transmitting quantum information. The fidelity of the quantum teleportation is discussed when an isotropic Heisenberg spin chain in a non-uniform magnetic field is used as a quantum channel. The expression of the fidelity of the quantum channel is derived by theoretical analysis. The effects of the inhomogeneity of the external magnetic field on the fidelity are investigated. It is found that the high fidelity can be achieved if the inhomogeneity of the magnetic field is small and the environmental temperature is low.