Research On Robustness Of Quantum Correlations Of Tripartite States

In quantum information theory, quantum entanglement is widely explored and applied as a kind of resource. However, quantum entanglement can not describe all the quantum correlations in the quantum system, because some non-entangled (separable) states can also be used for quantum information processing and have the advantage over the classical information processing. So the correlations are divided into classical and quantum, and the quantum correlations are used as resources for quantum information processing. In this paper, we first introduce the basic concepts of quantum information theory and a classification and corresponding characteriza-tion of quantum correlations on tripartite states, and define relative robustness of quantum correlations and robustness of quantum correlations, as well as their cal-culation. Based on these, we study the influence of the quantum channel on the robustness of quantum correlations on tripartite states. This paper is divided into three chapters, the concrete structure is as follows:In Chapter 1, we introduce the research significance and current situation of main content of this paper, some basic concepts and the definition and related properties of entanglement robustness.In Chapter 2, we study the characterization and quantification of quantum cor-relations on tripartite states. Firstly, we introduce the classification and judgment of correlations on tripartite states, prove that the set of all completely classically correlated states is compact. We give the necessary and sufficient condition for the convex combination of two completely classically correlated states to be still com-pletely classically correlated. Secondly, We define the relative robustness of quantum correlations on tripartite states due to the definition of entanglement robustness by Tarrach and Vidal. We prove the rationality of the definition and find a method to calculate the relative robustness of quantum correlations. Then we give the defini-tion of robustness of quantum correlations and further find a necessary and sufficient condition for the robustness of quantum correlations on tripartite states to be finite and prove the robustness of correlations is a lower semi-continuous function on the set of all quantum states of a tripartite system.In Chapter 3, we explore the influence of the quantum channels on the ro-bustness of entanglement and the robustness of quantum correlation on tripartite states. We obtain some necessary and sufficient conditions for a quantum channel to decrease (resp. increase, maintain) the robustness of quantum correlations of all tripartite states, and find some examples for each cases.