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The intersection operation in light of joint observables and Bell inequalities in operational probability theory

机译：结合概率和贝尔不等式在操作概率论中的交点运算

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摘要

Operational probability theory appears as a smooth extension of classical probability theory that fulfills quantum physics needs. In this paper, we, first, explain the need to extend the concept of the intersection operation in the light of the concept of joint observables. Then, we tried to determine the basic features that characterize any possible definition of the intersection operation. Furthermore, we tried to know if there is a relation between the definitions of the intersection operation of both fuzzy and operational probability theories. These relations are used, first, to find a suitable suggestion to define the intersection operation. Second, they are used, besides the studies made on Bell inequalities in fuzzy probability theory, to find the conditions that should be satisfied by the intersection operation to ensure the possibility of the violation of Bell inequalities in operational probability theory.
机译：操作概率论似乎是经典概率论的平滑扩展，可以满足量子物理学的需求。在本文中，我们首先根据联合可观测对象的概念来解释扩展相交操作的概念的必要性。然后，我们尝试确定基本特征，以表征相交操作的任何可能定义。此外，我们试图知道模糊和操作概率理论的相交运算的定义之间是否存在关系。这些关系首先用于找到定义相交操作的合适建议。其次，除了对模糊概率论中的贝尔不等式进行研究之外，还使用它们来找到交集运算必须满足的条件，以确保在操作概率论中违反贝尔不等式的可能性。

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