Research On Local Hidden Variable Theory And Quantum Correlation

Entanglement is one of the outstanding characteristic phenomena of quantum mechanics. This holistic property of compound quantum systems, which involves nonclassical correlations between subsystems, has potential for many quantum processes, including canonical ones:quantum cryptog-raphy, quantum teleportation, and dense coding. The main content of this thesis is research on entanglement and quantum non-locality. On one hand, 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 devel-opment of quantum non-locality; on the other hand, we show aspects of entanglement including its characterization, detection, quantification, and quantum non-locality inequality as a test of quantum entanglement. Mul-tipartite quantum states can be classified into local and non-local states or into separable (non-entangled) and entangled states. These two kinds of classification based upon Bell-type inequalities are not equivalent.To the qualitative aspects, Werner gave the detailed analysis and the typical examples-Werner states, one the quantitative point of view, the relations between entanglement quantity and the violation of CHSH inequality is also discussed in this paper. On the last of this thesis, we show relation-ship between the local commutativity and CHSH inequality violation. We track such path to describe the development of quantum non-locality and quantum entanglement,and discuss the intersection carefully.As to the manifestations of entanglement, we present a succinct in-equality for two-qubit quantum states reveal the non-locality and entan-glement. Furthermore, we extend relation between the local commutativity and CHSH inequality violation to3-qubit system,and shows that the con-verse trade-off relations do not always hold for three-qubit states, and that there exists some correlation even though the state is the simple product state.The thesis structured as follows:Chapter No.l We introduce the local hidden variable (LHV) theorem precisely, including the EPR disputation, Bohm model, the origin and the basic fundamentals of the LHV theory.Chapter No.2We first review the construction of Bell inequality and CHSH inequality, then describe Bell inequality on the general (2,2,d) case.Chapter No.3We introduce another kind of proof about non-locality, that is, all-versus-nothing violation of local realism, such as GHZ theorem, Hardy theorem and the Cabello’s contribution.Chapter No.4We first show fundamentals of quantum mechanics, in-cluding quantum state, density matrix, entanglement, criteria and quan-tification of entanglement, especially various manifestations of entangle-ment via Bell inequalities and the Wernrer discussion of classic correla-tions vs violation of Bell inequality. Then we discussion relation between the quantification of entanglement and the violation of Bell inequality.Chapter No.5We discuss the quantum entropic and the classical corre-lations.Chapter No.6We show the local commutativity and CHSH inequality violation on2-qubit case-conversed trade-off relations. Further more, we extended it to3-qubit case, and show the converse trade-off relations do not always hold for three-qubit states, and that there exists some correlation even though the state is the simple product state.