| It is well known that quantum entanglement is the most fascinating feature of quantum mechanics which has been studied intensively in recent years and is shown to play a key role in quantum information processing, such as quantum dense coding, quantum teleportation and quantum cryptographic key distribution. Due to their potential applications plus the scalability in quantum communication and information processing, the solid state systems have gained great attention. In particular, the spin chains, as the natural candidates for the realization of the entanglement, showed some substantial advantages compared with the other physical systems in quantum information processing. The Heisenberg spin chain, as the simplest spin chain, is used to construct a quantum computer based on many physical systems such as quantum dots, nuclear spins, electronic spins and optical lattices. In addition, by proper encoding, the Heisenberg interaction alone can support universal quantum computation. With these appealing properties, the Heisenberg spin chain has received much attention in the context of quantum information science.This dissertation is composed of five chapters and organized as follows. The first two chapters introduce the general development of quantum information theory and some fundamental knowledge relevant to quantum entanglement. Chapter 3 mainly investigates the entanglement of a three-qubit anisotropic Heisenberg XXZ ring with Dzyaloshinskii–Moriya (DM) interaction in thermal equilibrium at temperature T in the presence of an external magnetic field B along the z-axis and obtain analytic expression for the concurrence, in which the dependence of the concurrence on the anisotropic coupling coefficient Jz, external magnetic field B, the DM interaction parameter D and temperature T is described. The DM interaction is found to have a more significant role than the others in increasing the critical temperature or the entanglement area. And also calculates the ground-state entanglement under various control parameters and gives expressions for the quantum critical points at which quantum phase transition takes place. These results show that one is able to produce or increase the concurrence so that the efficient control of entanglement by appropriate combinations of the tunable parameters may be possible. Chapter 4 investigates the effects of different DM interactions on optimal dense coding with a two-qubit Heisenberg XXZ chain in external magnetic fields. The anisotropic coupling parameterΔ, isotropic coupling parameter J, and the DM interaction parameters are found to be effective for optimal dense coding, while the magnetic field turned out to be destructive. Moreover, the results show that the antiferromagnetic (AFM) case is more ideal for optimal dense coding than the ferromagnetic (FM) case in general. In the case of AFM, by the comparison of the two cases with the same fixed x- and z-component parameters of DM interaction (Dx and Dz), the appropriate model for optimal dense coding is indicated for the different value intervals ofΔ. Comparison of the effects of Dz and Dx on optimal dense coding is made and their dominant regions are clarified. Chapter 5 mainly investigates the effects of different DM interactions on thermal entanglement and teleportation of one-qubit state as well as the partial teleportation of an entangled state via a two-qubit Heisenberg XXZ spin chain under external magnetic fields. The DM interaction is found to be effective for the thermal entanglement for this model under external magnetic fields, while it turned out to be destructive for both single qubit teleportation and partial teleportation of a two-qubit entangled state. Moreover, the results show that only AFM chain is eligible for teleporting one-qubit state, while both AFM and FM chains are suitable for entanglement teleportation. In addition, the comparison of the effects of the same, fixed Dz and Dx on teleportation is presented.
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