New Type Bell Inequalities and Quantum Correlations

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The Bell inequality holds in the framework of the hidden variable theory and does not hold in quantum mechanics. Although failure of the Bell inequality has been known as a fact, a physical cause or a reason of the failure have not been understood clearly. In this study, I found that non-commutativity of local observables causes the violation of the Bell inequality. Taking this mechanism into account, I provided a method for systematic construction of generalized Bell-like inequalities and I formulated a new inequality that enables a fair test of the hidden variable theory and quantum theory.Moreover, via measurement theory I successfully derived superselection rules, which have not been justified nor derived from physical reasons for a long time. I found a necessary condition for a physical quantity to be measurable.Moreover, I cooperated on an experiment using spiral electron beam and successfully proved the uncertainty relation of angular momentum and the quantum eraser effect.