The Nonviolation Of Bell Inequality By Multipartite Entangled States

Quantum entanglement is a central concept of quantum mechanics,and can also be adopted as a physical resource for many quantum information processing tasks which cannot be achieve in a classical way.Nonlocality is a very profound concept in quantum mechanics,and the Bell inequality plays a central role in the research of quantum nonlocality and entanglement,and it has many applications in quantum information processing.In nature quantum mechanics is nonlocal,and incompatible with the theory of local hidden variables,which can be revealed by Bell inequality.Local realism theory constraints the correlations of measurement on multiparticle systems according to the form of Bell-type inequality.In a realistic theory,the measurement results are determined by hidden properties carried by the particles prior to and independent of observation.In other words,in local realistic theory,the results obtained at one location are independent of any measurements performed at spacelike separation.In this paper,we first research the necessary and sufficient conditions for W states to violate Bell inequality in local coordinate system,and study the case that the local coordinate system of 3-qubit and 4-qubit W states violated the Bell inequality after Euler rotation.In addition,we also research the violation of the Bell inequality by the generalized 3-qubit W state and the range of the parameters when the generalized 3-qubit W state satisfies the sufficient conditions that do not violate the Bell inequality after Euler rotation.The range of the parameters of the generalized 4-qubit W states in violation the Bell inequality after rotation has been also discussed.Finally,it is concluded that not all entangled pure states violate the Bell inequality.In chapter 1,we introduce some basic knowledge of quantum information.In chapter 2,we discuss and calculate in detail the nonviolation of Bell inequality in the local coordinate system（7）^?x^j,_y^??j（8）and the violation of Bell inequality in the local coordinate system（7）^?y^?j,_z^?j（8）,（7）^?x^j,_z^?j（8）for the N-qubit W states,where N=3,4,5,L.In chapter 3,we perform Euler rotation on the local coordinate system and study in details the conditions that 3-qubit,4-qubit W state violates the Bell inequality after rotation.In chapter 4,we mainly calculate the conditions that generalized 3-qubit W states does not violate the Bell inequality and generalized 4-qubit W states violates the Bell inequality after the rotation of the local coordinate system.