New Type Bell Inequalities and Quantum Correlations

贝尔不等式在隐变量理论的框架中成立，而在量子力学中不成立。虽然贝尔不等式的失败已经被认为是一个事实，但失败的物理原因或原因还没有被清楚地理解。在这项研究中，我发现，非交换性的局部可观导致违反贝尔不等式。考虑到这一机制，我提供了一种系统地构造广义Bell-like不等式的方法，并提出了一个新的不等式，使隐变量理论和量子理论得到了公正的检验，而且，通过测量理论，我成功地导出了超选择规则，这些规则长期以来都没有得到证明，也没有从物理原因推导出来。我找到了物理量可测量的必要条件，并合作进行了螺旋电子束实验，成功证明了角动量的测不准关系和量子擦除效应。

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.