作为量子概率演算的经典有限概率论
On classical finite probability theory as a quantum probability calculus
摘要：
本文展示了如何经典的有限概率论（等概率的结果）可以重新解释和重铸的量子概率演算的教学或“玩具”模型的量子力学集（QM/集）。以前有四次尝试用$\mathbb{Z}_{2}$代替$\mathbb{C}$的基场来建立类量子模型，但它们都被要求方括号取$\mathbb{Z}_{2}$中的值（1 =可能，0 =不可能）而被迫变成仅仅是“模态”的解释。但通常的QM括号<|给出了状态A和A之间的“重叠”，因此对于U的子集S，T，自然定义是$<S|T>=|S{\cap}T|$。这使得QM/集可以用一个完全概率演算来开发，这个演算被证明是完美的经典拉普拉斯-布尔有限概率理论。重点不是澄清有限概率论，而是通过看到它的一些量子特征来阐明量子力学本身（例如，双缝实验）中的经典设置。
英文摘要：
This paper shows how the classical finite probability theory (with equiprobable outcomes) can be reinterpreted and recast as the quantum probability calculus of a pedagogical or "toy" model of quantum mechanics over sets (QM/sets). There have been four previous attempts to develop a quantum-like model with the base field of $\mathbb{C}$ replaced by $\mathbb{Z}_{2}$, but they are all forced into a merely "modal" interpretation by requiring the brackets to take values in $\mathbb{Z}_{2}$ (1 = possible, 0 = impossible). But the usual QM brackets <ψ|ϕ> give the "overlap" between states ψ and ϕ, so for subsets S,T of U, the natural definition is $<S|T>=|S{\cap}T|$. This allows QM/sets to be developed with a full probability calculus that turns out to be the perfectly classical Laplace-Boole finite probability theory. The point is not to clarify finite probability theory but to elucidate quantum mechanics itself by seeing some of its quantum features (e.g., two-slit experiment) in a classical setting.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
