The Realization Of The Super Dense Coding In A Two-qubit Heisenberg XY Model And Three-qubit Heisenberg XXZ Model

As a physical resource entanglement state plays an important role in quantum information field, such as quantum teleportation，quantum key distribution, quantum computing etc. Quantum entanglement is the basis of quantum information theory, and prerequisite for realization of quantum communication and quantum computing. Quantum dense coding can be considered as one of hottest research topics, which attracts many people’s attention. Quantum densecoding is one of the hot topics of attention in quantum information. Due to their potential applications plus the scalability in quantum communication and information processing, the solid state systems have gained great attention. Inparticular, the spin chains, as the natural candidates for the realization of theentanglement, 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 spinsand 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 contextof quantum information science.This dissertation is composed of five chapters and organized as follows.The first two chapters introduce the general development of quantum informationtheory and some fundamental knowledge relevant to quantum information. The third chapter introduces the basic concepts, principles and history of the development of quantum dense coding. The fourth chapter mainly studies the effectof magnetic field and DM interaction to the realization of quantum dense coding in the two-qubit Heisenberg XY spin chain model. Through the dense coding channel capacity formula, we calculated the analytical expressions of the channel capacity of the quantum dense coding and analyzed the relationship between the dense coding channel capacity and other parameters. We make a comparison the effects of uniform magnetic field B, the non-uniform magneticfield b, the anisotropy parameter J and DM interaction to the optimal dense coding, and found that the DM interaction and anisotropy parameters playsan active role to the dense coding, but the uniform magnetic field, the non- uniform magnetic field plays a negative role to the dense coding. In the fifthchapter, we study the effects of the external magnetic field on the quantumdense coding in the anisotropic three-qubit Heisenberg XXZ model, through the analytical expressions of the channel capacity in the quantum dense coding,we analyzed the influence of coupling constant J，external magnetic field B,anisotropy parameterJ zand the temperature T on the quantum dense coding.The results showed that B，J z， J have a positive effect to dense coding at finite temperature in this model. These results indicate that the quantum dense coding channel capacity can be improved by appropriately combining thesecontrollable parameters in order to achieve optimal quantum dense coding.