Research On LHV Theory And Quantum Non-locality From The Viewpoint Of Correlation

Quantum non-locality is not only an foundation problem of quantum theory,but also plays an important significance on quantum information processing,such as quantum computation,quantum communication and quantum cryptography security.The main content of this paper is research on LHV theory and quantum non-locality from the viewpoint of correlation.From the EPR paradox leading to oppugn for quantum mechanics,to the institution of local hidden variable theory,until Bell inequality and Bell theorem without inequalities,we track such path to describe the development of quantum non-locality.As to the promotion and construction of Bell type inequalities, we present a systematic approach to construct non-homogeneous Bell-type inequalities. For Bell theorem without inequalities,we extend such proof for generalize GHZ states and W states.Furthermore,we extend Greenberger-Horn-Zeilinger(GHZ) argument of nonlocality without inequalities to the case of four-qubit mixed states.The thesis is structured as follows:Chapter No.1 We introduce all types of correlations,such as,generalized correlation, no-signaling correlation,local correlation,partial-local correlation,and quantum correlation.Chapter No.2 We give a precise description about local hidden variable(LHV) model.In this chapter,we introduce the EPR disputation,Bohm model,Von Neuman's proof about no dispersion-free state,Gleason theorem in detail.Multi-partite local hidden variable model also defined.Chapter No.3 In this chapter,we firstly introduce Bell's oppugn about Von Neuman's view.Then,we review the construction of Bell inequality.Several famous Belltype inequalities are also referred,such as,CHSH inequality,MABK inequality,and WWZB inequality etc.The third,we present a method to construct non-homogeneous Bell-type inequalities in detail,which is one of the most important work in my doctoral career.Chapter No.4 We introduce another kind of proof about non-locality,that is,allversus nothing violation of local realism.Followed such track,we firstly introduce GHZ theorem.Then,Hardy's model is presented in detail.We also introduce Cabello's contribution on all-versus-nothing proof,Finally,we extend all-versus-nothing proof to four-qubit mixed states.Chapter No.5 We discuss the connection between LHV model and noncommutativity in detail.Chapter No.6 conclusions.