Theoretical Study On Dynamics Of Quantum Correlation

Quantum information and quantum computation(QIQC) is an interdiscipline in-volving quantum mechanics, information and computation science, which can be traced back to the1980s. Considerable progress on quantum algorithm, quantum cryptography and quantum communication has been achieved since then. Notably, quantum entangle-ment, as an essential resource and ingredient of QIQC, has attracted much attention from physicists. It was considered that quantum correlation was exactly quantum entangle-ment, but more and more researchers now recognize that quantum entanglement is just one special kind of quantum correlations, and find that the unentangled state containing quantum correlation can be used to implement the tasks that classical computation fails to achieve.Quantum computer is designed by employing the coherence of quantum state. However, due to decoherence, quantum coherence in quantum computation will in-evitably decrease, even vanish. The research on decoherence will contribute to imple-mentation in quantum computation. The dynamics of quantum correlation refers to the time evolution of quantum correlation, researches on which will provide a better un-derstanding of both quantum correlation and existing problems in quantum information processing. Therefore, in the thesis we mainly study the dynamics of quantum cor-relation under different decoherence environments. The main content of the paper is organized as follows:1. We study the dynamics of correlation under the spin chain environment. Firstly, the dynamics of correlation for a central two-qubit system coupled to an Ising spin chain is investigated, where quantum correlation is quantified by both quantum discord and geometric measure of quantum discord(GMQD). It is found that the two measures can be used to detect the quantum phase transition point of Ising spin chain under the weak-coupling condition. There exists a sudden transition between quantum discord and clas-sical correlation near the phase transition point under the evolution. GMQD keeps un-changed for some initial states. Secondly, we consider the dynamics of correlations for a hybrid qubit-qutrit system in an XY spin-chain environment with Dzyaloshinsky-Moriya(DM) interaction. Quantum correlation is measured via quantum discord and measurement-induced disturbance(MID), respectively. In order to compare with the behaviors of quantum correlations, we also focus on the dynamics of entanglement, measured by negativity. The expressions of negativity, quantum discord and MID for a class of states can be calculated analytically, respectively. It is found that quantum discord is optimal among the three measures to detect the critical point of quantum phase transition. DM interaction does not affect QPT induced by the external magnetic field and only enhances the decay of quantum correlations. When only the qubit in-teracts with the environment, the phenomenon of sudden transition between classical correlation and quantum discord is observed. Entanglement suffers sudden death while quantum discord and MID decay asymptotically.2. We study the dynamics of quantum correlation for qutrit-qutrit states under depolarizing and dephasing noise, in which GMQD is used to quantify quantum cor-relation. Firstly, the dynamics of quantum correlation for a family of bound-entangled states is investigated. The decay rate of quantum correlation under depolarizing noise is slower than that under dephasing. Secondly, quantum correlations for a class of particu-lar initial states exist a sudden change near the transition point from bound-entangled to free-entangled state. The sudden change point remains unchanged in the later evolution under local and multilocal depolarizing noise. The behavior of quantum correlations is independent of the parameter of given initial states in many regions. However, the phe-nomenon does not exist under local dephasing noise, and it only occurs under collective dephasing. Thirdly, it is found that local transformation for the previous states does not change the behavior of quantum correlations under depolarizing noise, but it slows the decay of quantum correlations. Finally, we investigate the dynamics of quantum corre-lations for the Werner-like state and find that quantum correlations tend to be different constants under collective dephasing and local depolarizing noise.