Quantum Correlation Evolution Of A Two-Qubit Heisenberg Spin Chain With Dzyaloshinski-Moriya Interaction In An Inhomogeneous Magnetic Field

Quantum communication is a research hotspot of quantum information science,and quantum correlation is an essential resource in quantum communication.The Heisenberg spin chain in solid spin system is an important carrier to realize quantum correlation.However,the decoherence between the system and the environment will lead to the attenuation of the quantum correlation,so it is very necessary to prevent or reduce the interference of the environment on the quantum correlation.In this paper,the diffusion method of non-Markov quantum states with environmental memory characteristics is used.This method can not only accurately study the singularity of non-Markov processes,but also improve the computational efficiency.In this paper,the quantum correlation properties of the Heisenberg spin model are studied by using the diffusion method of non-Markov quantum states.The evolution properties of the quantum correlation are analyzed by adjusting the non-Markov degree(environmental memory effect coefficient),Dzyaloshinski-Moriya interaction,magnetic field strength,coupling coefficient and other controllable parameters.It provides a theoretical basis for the study of quantum correlation evolution of solid-state quantum spin system.The thesis is divided into four chapters.The first chapter introduces the development history of quantum information and the basis of topic selection.The second chapter introduces the diffusion method of non-Markov quantum states and the theoretical knowledge of quantum correlation.In the third chapter,we study the quantum correlation evolution of Heisenbergxx spin chain in an inhomogeneous magnetic field.The results show that the quantum correlation is obviously improved under the strong non-Markov effect,especially for the quantum entanglement.The effect of coupling coefficient on quantum correlation is different in different states.When the Dzyaloshinski-Moriya interaction increases,the system correlation will also increase,and it is close to the ideal value of1.The magnetic field has a positive effect on the quantum correlation,and the non-uniform magnetic field has a more obvious effect on the quantum correlation.Quantum entanglement is the optimal quantum correlation.In chapter 4,we study the quantum correlation evolution of the Heisenberg XXZ spin chain in an inhomogeneous magnetic field.The results show that the longer the environment memory time,the longer the survival time of quantum correlation;The effects of the coupling coefficients in different directions on the quantum correlation are different,and the effects of the coupling coefficients in different states are also different.The Dzyaloshinski-Moriya interaction has a positive effect on the quantum correlation,which makes the quantum correlation no longer decay,but oscillates with time.However,when the DM interaction is equal to 1,quantum phase transition exists in the quantum entanglement.The magnetic field has a positive effect on the quantum correlation,and the quantum correlation can reach the ideal value of 1 under the magnetic field.