Research On Quantum Steering And Its Robustness

As an important physical resource,EPR steering is of great value in the field of quantum information.It has become one of the hot topics in the research of quan-tum mechanics.EPR steering is a kind of important quantum nonlocality which was proposed by Schrodinger in the study of the EPR paradox,it describes the effecting ability of measuring on one particle to another which can’t be explained by LHS.EPR steering is a quantum correlation between quantum entanglement and quantum nonlocality.According to this theory,quantum steering has the charac-teristics of asymmetry,and there exists one-way quantum steering,that is,one side can successfully steer the other side,but in turn it does not.In this paper,we discuss the properties of the unsteerable and the absolute-ly unsteerable quantum states and the steering robustness and absolute steering robustness of bipartite states.The thesis article is divided into three parts,the specific structures are as follows.In Chapter 1,we introduce some research background and current situation of the topic and list some basic concepts and existing results used in the paper.In Chapter 2,we introduce the concepts of quantum steering of bipartite states and give a characterization of a unsteerable state.We prove that the set of all unsteerable states is closed and convex in the set of all states and that a local channel transforms all unsteerable states as unsteerable ones.Based on these results,we propose a method of quantifying quantum steering,called steering robustness and show many properties about it.By using the majorization between respective reduced states of two pure states,we can compare the steering robustness of the two states.Moreover,we prove that every maximally entangled state is maximally steerable.In Chapter 3,we define the absolutely unsteerable states and get some related properties.Finally,we propose the definition of the absolute steering robustness of two states and explore some key properties about it.