Researches On Various Correlations In An Open Heisenberg XYZ Spin Chain Model

The solid system aroused the interest of many researchers in the field ofquantum information, because solid system is easy integration and scalabilityin information processing, so it has the potential applications of quantum communication. Most of all，spin chain has been considered the best candidate system for achieve quantum entanglement. In quantum information processing, thespin chain system has a great advantage compared with other physical system. Heisenberg model is an effective model to describe many physical systems,such as nuclear spin, electron spin, quantum dots and quantum optical lattice,etc.. If we properly encoded, you can achieve any logic circuit quantum computing. Because the Heisenberg spin chain has many remarkable properties, it has potential applications in quantum information science.This thesis mainly studied around the various correlations in two-qubits Heisenberg spin chain model, mainly including the following contents：In first two chapters，we brief introduce the history of the development ofquantum information theory as well as the basic concepts and practical application ofvarious correlations. In third chapter，we study the two-qubits Heisenberg XYZ andXX spin chain model with Dzyaloshinskii-Moriya (DM) interaction, and calculatedtheir analytical expression. It can be seen that the thermal entanglement depends onthe coupling constantJ x, J y,Jz,J, along the Z direction of DM interactionDzparameters and temperature T. The results show that in a limited temperature range,to increase the quantum correlations the DM interaction parameter take greater rolethan the other parameters, especially in the XX model. The thesis also calculates thevarious correlations expression when parameters take different values and only giventhe analytical expression for the concurrence. We found that by appropriatelycombining these adjustable parameters can be generated and improve the quantumcorrelation. In the fourth chapter， we study case of exist phase decoherenceHeisenberg XYZ model with DM interaction. The results show that in the presenceof phase decoherence case the DM interaction plays a destructive role to the variouscorrelations, it is opposite compared with thermal equilibrium case. In addition, inthe time evolution of quantum entanglement and quantum discord show thewell-known phenomenon such as “collapse " and " revival ". However, to phasedecoherence the quantum discord more sensitive than quantum entanglement，because we take optimized combination of the system parameters in the whole process, so the adverse effects of phase decoherence to various correlations canavoided in some extant.