Investigation Of Non-Markovian Dynamics Of Two-level Open Quantum Systems

The study of open quantum systems is of great importance in quantum informa-tion and computation. There are various miracle phenomenon in non-Markovian process due to the existence of the memory effect of the environment, such as the oscillation of the trace distance and the quantum entanglement. Therefore, the study of the non-Markovian dynamics is significant in both theory and prac-tical applications. In this paper, we study the non-Markovian dycamics of a set of different open quantum systems by using the time-convolutionless projection method. We focus on questions of the non-Markovianity measures, the effects of environmental factor on the non-Markovianity of the open quantum processes and the influence of non-Markovianity on quantum information transmission.The paper is structured as follows.The first chapter is an introduction of the background knowledge. Some basic matters of the open quantum system are recommended, including the dynamical maps of open quantum process, the definitions of quantum Markovian process and quantum non-Markovian process, the time-convolutionless master equation and same typical non-Markovianity measures. Some physical quantities like concur-rence, quantum discord and mutual information are introduced briefly.In the second chapter, three typical non-Markovianity measures are compared by studying the non-Markovian dynamics of the two-level system in three basic noisy model. We find that three measures are equivalent when the master equation of the system contains only one decay rate but unequivalent when the number of the decay rates is larger than one. Moreover, the effect of the non-rotating term on the non-Markovian dynamics of the system is considered and it is indicated that the rotating wave approximation is invalid when the width of the spectral density or the detuning between the system and the environment is large.In chapter three we study the non-Markovian dynamics of a two-level system coupled to a compound noise model containing amplitude noise and phase noise. The numerical simulation shows that the interference of the two noises will reduce the non-Markovianity of the system dynamics, and there are only two possible optimal initial state pairs for the non-Markovinanity measure. By comparing with the two single noise models, we conclude that the non-Markovianity of the open quantum process is mainly dominated by the phase noise.In chapter four, we study the relation between the initial environmental coherence and the non-Markovianity of the open quantum system, and shows that the initial environmental coherence does not affect the quantity of the non-Markovianity. We also consider the revolution of the system-environment corre-lation, the environmental coherence and the information flow. We find that the increase of the system-environment correlation is not necessarily related to the decrease of the information of the system, the information can be stored either in system, environment or their correlation.In chapter five, we study the transmission of quantum information through a moisy spatial quantum channel (SQC). We find, for the non-Markovian or time-dependent Markovian noise, by breaking SQC into a series of periodically arranged subcomponents, that the quality of information transmission can be improved. The method is also valid for quantum information storage.The last chapter is the conclusion and overlook of the paper.