Quantum Correlation Dynamics Of Heisenberg XYZ Spin Chains In Non-Markov Environment And Cosine Magnetic Field

Since Feynman proposed the concept of quantum computing,the quantum computing technologies and the matching quantum communication technologies have also been developed.After nearly 40 years of development,the researchers have found that the physical systems that can realize quantum computing and quantum communication include:semiconductor quantum dots,superconducting Josephson junction,topological superconductivity,ion trap,nuclear magnetic resonance,Heisenberg spin chain,etc.The Heisenberg spin chain has good integration,scalability,stability and easy realization.However,in practical situations,any quantum system we study will be affected by the surrounding environment,which usually produces noise to destroy the correlation properties of the quantum system even if the quantum system has a decoherence process.Therefore,it is very meaningful to study the evolutionary dynamics of quantum correlations of quantum systems in open quantum systems.There are many methods to study open quantum systems,such as quantum Liouville equation,projection operator technique,fluctuation dissipation principle,master equation method,quantum state diffusion method,stochastic Schrodinger equation,Feynman-Vernon response functional theory,density functional method and Langevin equation.The environment of an open quantum system can be divided into a Markov environment with no memory effects and a non-Markov environment with environmental memory effects.When the interaction between the quantum system and the environment is weak,the quantum system is in the Markov environment,and the evolution of the system correlation dynamics can be obtained by solving the Markov master equation and the Langevin equation.However,only the non-Markov master equation can meet the real evolution process.The non-Markov quantum state diffusion method is a very useful method proposed by Diosi,Gisin and Strunz in 1998 for handling open quantum systems,which has proved to be the most powerful tool for studying system dynamics.The main idea is to decompose the evolution of a quantum state into the evolution of many quantum trajectories,and then to average the ensemble of the system to obtain the approximate density matrix of the system.There are many advantages when solving the master equation of density operators by quantum trajectories.Specifically,in the existence of large quantum fluctuations with the original method is difficult to deal with and use the present method is easy to solve;Secondly,it has embedded the dynamic theory in the quantum measurement,and a random quantum trajectory can match a monitoring process,so that we can know some specific cases in the evolution process.In this paper,we solve the non-Markov master equation to calculate the reduced density matrix of the anisotropic Heisenberg XYZ spin chain,and then bring the time-evolving reduced density matrix into the correlation formula of quantum correlation,and simulate the evolution of the correlation dynamics by using MATLAB numerical calculation software.In this paper,the initial state of the quantum system is on the maximum entangled state,and the correlation characteristics of the quantum system are improved by changing the internal and external parameters of the system to better serve the field of quantum information and quantum computing.Studies show that the strong non-Markov characteristics,that is,the smaller environmental correlation coefficient?,can increase the correlation characteristics of the system;The stronger the non-Markov properties,the stronger the environment is to recover to the earlier state,thus significantly improving the correlation properties of the system during evolution.The correlation properties of the system improve very significantly with the larger the spin coupling coefficient J,which is determined by the structure of the anisotropic Heisenberg XYZ spin chain.The quantum correlation of the system can also be significantly increased when the timevarying magnetic field intensity B is large,indicating that the magnetic field intensity can effectively improve the quantum correlation of the quantum system.In addition,regulating other parameters in a certain range also has a certain effect on the quantum correlation properties of the system.In conclusion,the anisotropic Heisenberg XYZ spin chain can be realized by reasonably regulating the internal and external parameters of the system,keeping the quantum correlation characteristics of the system at a high level during evolution.Improve the quantum correlation characteristics of the quantum system can make the coherence characteristics of the system is not destroyed for a long time,namely improve the coherence time of the system,so as to better study quantum computing and quantum communication services,and for researchers from the experiment in a long time can maintain high correlation characteristics of the quantum system provides theoretical guidance.