The Entanglement Measure And Violation Of Bell Inequality

Entanglement is not only a unique element to expose the singularity of quantum mechanics,but also a potentially valuable resource.Quantum entanglement plays an important role in the quantum information processing.Bell inequality can characterize the possible relationship between quantum violation and quantum entanglement,so it is of great significance for using Bell inequality to study quantum entanglement.Based on Bell inequality we conclude that the locally hidden variable model cannot realize all the predictions of quantum mechanics,which has a profound impact on our understanding of physics.In local realism theory,the measurement results of any observable must be determined by hidden variables,which are not affected by the measurement of another subsystem under the spacetime interval.In this paper,we first calculate the violation of Bell inequality by the W-type state of 3-qubit,then calculate the 3-ME concurrence of this state,and observe that there is some relation between them.And then we calculate the violation of Bell inequality for the W-type state of 4-qubit,and calculate the 4-ME concurrence for the state,and observe some connection between them.The relations between the violation of Bell inequality and ?-ME concurrence for any3-qubit and two Dicke states are then discussed.The first chapter is about some basic concepts and basic knowledge of quantum information used in this paper,including entangled state,reduced density operator,CHSH inequality and so on.In chapter two,the violations of the Bell inequality in three sets of local coordinate systems are obtained for the W-type state of 3-qubit and the W-type state of 4-qubit.We deduce the condition of the coefficients of states violating the Bell inequality.The relationship between the violation of Bell inequality and entanglement of the states is obtained.In chapter three,we consider any 3-qubit state,first we calculate the form of 3-ME concurrence for any 3-qubit state,and then we give in detail the conditions for any 3-qubit state to satisfy the violation of Bell inequality in three sets of local coordinate systems,as well as the relationship between violation of Bell inequality and entanglement of quantum states.In chapter four we discuss two Dicke states.The violations of Bell inequality in the local coordinate system for these states are obtained.Finally we summarize the results of each chapter.