| As an branch of physics, the quantum mechanics was constructed in20th century for studying physical phenomena where the action is on the order of the Planck constant. The understanding on physical phenomena at the atomic and subatomic scales does not only deepen by studying of quantum physics, the development of the science and technology was also improved greatly. Recently for the development of quantum information theory, the study on the basic theory of quantum theory and the realization in laboratory was highly valued. For the real condition in laboratory, the quantum system is always open and interacts with surrounding inevitably., so as to the energy and some special character of quantum system will loss into the environment.In this thesis, we will focus on the issue of the open quantum open system. By means of master equation, we investigate the influence of the geometric phase and the quantum correlation on the effect of the coupling with environment. And then, we show the existence of the time-dependent decoherence-free subspace. in which the protection and the manipulation of quantum state could be achieved at the same time.This thesis consists of three parts. In the first part, i.e., Chaps.2, we introduce the fun-damental conceptions and methods which are relative to our work. Firstly, we introduce the definition of density matrix. As main method for describing the open quantum system in this thesis, we derive the Markvoian master equation under the Born-Markovian approximation by means of Nakajima-Zwanzig project operator technique and an kind of time-local non-Markovian master equation by means of time-convolutionless projection operator technique. And then we review some definition in quantum theory related with our work, i.e., quantum discord, the geometric measurement of quantum discord, technique for engineering reservoir, decoherence-free subspace and geometric phase.Part two is composed of Chaps.3and Chaps.4, in which the effect of the coupling between the quantum open system and the environment on the geometric phase and the quantum dis-cord are investigated. In Chaps.3, Geometric phases and information flows of a two-level system coupled to its environment are calculated and analyzed. The information flow is defined as a cumulant of changes in trace distance between two quantum states, which is similar to the measure for non-Markovianity given by Breuer. We obtain an analytic relation between the geometric phase and the information flow for pure initial states, and a numerical result for mixed initial states. The geometric phase behaves differently depending on whether there are information flows back to the two-level system from its environment. In Chaps.4, we study the dynamics of quantum discord and explore the relation between the entanglement sudden death and QDSC. We find that the QDSC is sensitive to the initial states and the excitation number in the total system (the qubits+environment). By using the geometric measurement of the quantum correlation, the geometric interpretation for the QDSC is pre-sented and the condition for the emergence of the QDSC is given. Furthermore, we observe that the entanglement sudden death and QDSC do not have one to one correspondence for open quantum systems.Chaps.5by itself consists of the third part of this thesis. With time-dependent Lindblad operators, an open system may have a time-dependent decoherence-free subspace (t-DFS). In this paper, we define the t-DFS and present a necessary and sufficient condition for the t-DFS. Two examples are presented to illustrate the t-DFS, showing that this t-DFS is not trivial, when the dimension of the t-DFS varies.Finally, the conclusions and discussion are given. |
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