The Study Of Thermal Entanglement And Its Application In Spin Chain Systems

As an important resource of quantum information and quantum computing,quantum entanglement has been widely used in quantum teleportation,quantum dense coding and quantum key distribution.Known as a simple and practical model for describing solid state systems,Heisenberg spin chain model is one of the most promising physical systems for realizing quantum information and quantum computing.Due to a real physical system in the real environment can not always be in the ground state,but usually in a thermal equilibrium state at a certain temperature,therefore,it is very important to study entanglement and its application in the thermal state.Based on the Heisenberg spin chain system,we theoretically investigate the properties of thermal entanglement and its application to quantum state teleportation in one-dimensional spin chain systems.1.We study the thermal entanglement of XXZ model with DM interaction under topological and periodical boundary conditions.By considering DM interaction alonging z,x and y directions in the three-qubit XXZ model,we research the changing behaviour of the bipartite thermal entanglement Concurrence and tripartite thermal entanglement Negativity with temperature,Heisenberg interaction strength and anisotropy parameter in the topological boundary and periodical boundary conditions.The results show that the bipartite thermal entanglement and tripartite thermal entanglement have different behaviors when DM interaction is in different directions under topological boundary conditions.However,for the periodical boundary condition,the different DM interaction directions have no effect on the change of bipartite thermal entanglement.Fortunately,the DM interaction can induce bipartite thermal entanglement and increase the critical temperature of bipartite entanglement.2.We investigate the effect of impurities on the thermal entanglement in a spin-1/2infinite Ising–Heisenberg butterfly-shaped chain.By using the transfer-matrix approach and the reduced density matrix,we numerically calculate the bipartite thermal entanglement concurrence of the nearest-neighbor and the next-nearest neighbor Heisenberg spins,which are located in the intermediate unit block of two blocks with impurities.And the effects of uniform distribution and Gaussian distribution of impurity parameters on entanglement are also discussed.Considering the effects of the external magnetic field,temperature,Heisenberg and Ising interactions as well as the parameter of anisotropy on the thermal entanglement,our results reveal that comparing with the case of the clean model,in both the two impurity model and the impurity fluctuation model the entanglement is more robust within a certain range of anisotropic parameters and the region of the magnetic field where the entanglement occurs is also larger.3.We investigate the teleportation of the entangled state through a couple of quantum channels of the anisotropic Ising-XYZ diamond chain.We calculate the density operator of quantum channel by using the transfer-matrix approach and give the output entangled states under the influence of different input concurrence values,temperature,magnetic field and Heisenberg interaction parameters according the standard teleportation protocol by considering the initial pure state of two qubits.Moreover,the effects of the temperature,Heisenberg interaction,XY-anisotropy coupling parameter as well as the external magnetic field on the average fidelity are studied.The results show that low temperature is beneficial to the transmission of entangled states,the input concurrence and Heisenberg interaction can enhance the output concurrence,while the strong magnetic field will inhibit the output entanglement.In addition,the Heisenberg coupling parameter can also increase the average fidelity,however,high temperatures,strong magnetic fields,and larger XY-anisotropy parameter will restrict the transfer.