Research On Quantum Correlations In Werner Derivatives And WLQCC States

Quantum information science is an inter-discipline of quantum mechanics and information science. Quantifying the quantum correlations in quantum states and exploring its regular of changing undergoing particular operations are the hot research fields in the discipline recently. This thesis has five parts. In the preface the author introduces some concepts in quantum mechanics and information, the present development of domestic and international study. In the following three sections, the author detailedly states his own researches during the period he worked for his master degree. They comprise the study on the quantum correlations in two-qubit and two-qutrit Werner states under nonlocal unitary operations, the study on the quantum correlations in two-qubit Werner states under local nonunitary operations. Afterwards, a brief summary is given at the end. The main research works included in this thesis are as follows:1. Werner derivatives are a special kind of mixing states transformed from Werner states by unitary operations [Phys. Rev. A62,044302(2000)]. The inherent quantum correlations in Werner derivatives are quantified by two different quantifiers, i.e., quantum discord [Phys. Rev. A88,017901(2001)] and geometric discord [Phys. Rev. A105,190502(2010)]. Different analytic expressions of the two discords in Werner derivatives are derived out. Some distinct features of the discords and their underlying physics are exposed via analyses and discussions. Moreover, it is found that the amount of quantum correlations quantified by either quantifier in each derivative can not exceed that in the original Werner state. In other words, no unitary operation can increase quantum correlation in a Werner state as far as the two quantifiers are concerned.2. The inherent quantum correlations in two-qutrit Werner states undergoing local and nonlocal unitary operations are studied by two different methods, i.e., quantum discord and measurement-induced disturbance (MID)[Phys. Rev. A77,022301(2008)]. A same analytic expression of the two kinds of quantum correlations in the derivative states is derived out. Some distinct features of the correlations and their underlying physics are exposed via analyses and discussions. Moreover, it is found that the amount of quantum correlations quantified by either quantifier in each derivative state can not exceed that in the original Werner state. In other words, no unitary operation can increase quantum correlation in a two-qutrit Werner state as far as the two methods are concerned. 3. WLQCC states are the states mapped from Werner states by single-state LQCC (local quantum operations and classical communication) protocols. Quantum discords in the WLQCC states are studied and nineteen parameters involved are reduced to four parameters in terms of properties of Werner states and discord. In the case of orthogonal projective measures, analytic expression of discords in WLQCC states is worked out. By virtue of numerical computations, quantum discords in a Werner state before and after LQCC are compared. It is found that quantum discord in any WLQCC state cannot exceed that in the original Werner state.