Quantum Steering Research Of Bell-diagonal States Based On Semidefinite Programming

The development of quantum communication technology will be paid more and more attention with the launch of "Mo Zi",an experimental satellite of quantum science.The realization of quantum communication depends on the different kinds of nodes with various communication capabilities and the quantum entanglement effect that produce from the basic particles such as photons.Quantum steering is a special kind of quantum correlation between quantum entanglement and Bell nonlocality,which is one of the core resources of quantum information,and describes a pair of entangled particles,which one part can measure the particles and achieve "steering" phenomenon for the state of other particles of the other party.So it is self-evident that quantum steering research for the importance of quantum network communication.The quantum steering of the Werner states in the two-qubit system has been completely solved,but the research on the slightly complex Bell-diagonal state is far from enough.Although the steering characteristics of two-qubit Bell-diagonal states by two and three projective measurements operators have been studied,the range of steering is different because of the diverse projective measurements operators,the research of Bell-diagonal states steering has not involved the investigation and research of other projective measurements operators(operators number n=4,6,8,10).In this paper,we introduce the definition of quantum steering,the basic knowledge of quantum computation,quantum steering ellipsoids and the application form of semidefinite programming in quantum steering.At the same time,we make a brief introduction of the criterion about the steering of two-qubit system Bell-diagonal states by two and three projective measurements operators.We choose the polyhedron to construct the projective measurements operators,and shed light on takeing advantage of the semidefinite programming(SDP)method to solve the steering problem of Bell-diagonal states based on other projective measurements operators by matlab programming and calculation.We explore the SDP method by the forms of the list and figures to modify and improve continuously the scope of the Bell-diagonal states based on the other projective measurements operators.Finally,we accomplish the quantum steering problem of noise Bell states,and the lower rank states with four parameters through this method.