Quantum Information In Open Quantum Systems

Over the past several decades, quantum information science has become a fast developing discipline. The interaction between quantum systems and envi-ronment brings great difficulties to the implementation of quantum information processing. So we do researches on the quantum information in open quantum systems.This dissertation focus on the quantum coherence, quantum correlation and quantum Fisher information in the open quantum systems. The structure of this dissertation is arranged as follows.Chapter 1 gives a short introduction on the quantum information science and the outlines of this dissertation.Chapter 2 introduces some basic concepts in the quantum information sci-ence, especially the frequently-used measures of entanglement and correlation, as well as two paradigms of the classification of correlation.In Chapter 3, we introduce the operator fidelity and operator fidelity sus-ceptibility based on the reference state, construct the Riemannian structure on the manifold of unitary operators. We will see that these rather abstract math-ematical structure are strongly related to the decoherence factor in the purely-dephasing model. We also discuss the impact of the quantum criticality of the environment on the operator quantum geometric tensor and decoherence factors.In Chapter 4, we investigate two questions. The one is the optimal mea-surements accessing the classical correlations, and the other is the decay of the quantum discord under decoherence. For the first question, we propose an effec-tive approach, which can hit the optimal measurements with a great probability. The efficiency of this approach is also investigated. Furthermore, we introduce a upper bound of quantum discord. For the second question, we will see that the geometric measure of quantum discord may not reflect the decay modes of the quantum discord. However, we will prove that at least for the Bell-diagonal states, the geometric measure of quantum discord can correctly reflect the decay mode of quantum discord.In Chapter 5, we discuss the quantum Fisher information of open quantum systems. We clarify some basic ideas, e.g. "memory" and "information", in the non-Markovian dynamics. We introduce the concept of quantum Fisher informa-tion flow, through which the non-Markovianity is interpreted as the inward flow of quantum Fisher information. We also point out that not only the system and the environment can store Fisher information, but also the correlation between them could. A measure of the information stored in the quantum correlation is also introduced.Chapter 6 denotes the conclusion and prospect.