论文标题
与叠加事件的概率理论：量子力学方向的经典概括
Probability Theory with Superposition Events: A Classical Generalization in the Direction of Quantum Mechanics
论文作者
论文摘要
在有限概率理论中，事件是结果集的子集。子集可以用一维柱向量表示。通过将事件的表示形式扩展到二维矩阵，我们可以引入“叠加事件”。使用密度矩阵引入了用于经典事件，叠加事件及其混合物的概率。然后，可以像使用密度矩阵在量子力学（QM）中确定所有这些事件的实验或“测量”的概率。此外，通过实验或“测量”引起的密度矩阵的转换是Luders混合物的操作，如QM所示。最后，通过将机械移至Z_2上的N维矢量空间中，不同的基础集成为不同的结果集。有限概率理论的“非交通性”扩展产生了量子力学的教学模型，可以模拟QM的许多特征非经典结果。
In finite probability theory, events are subsets of the outcome set. Subsets can be represented by 1-dimensional column vectors. By extending the representation of events to two dimensional matrices, we can introduce "superposition events." Probabilities are introduced for classical events, superposition events, and their mixtures by using density matrices. Then probabilities for experiments or `measurements' of all these events can be determined in a manner exactly like in quantum mechanics (QM) using density matrices. Moreover the transformation of the density matrices induced by the experiments or `measurements' is the Luders mixture operation as in QM. And finally by moving the machinery into the n-dimensional vector space over Z_2, different basis sets become different outcome sets. That `non-commutative' extension of finite probability theory yields the pedagogical model of quantum mechanics over Z_2 that can model many characteristic non-classical results of QM.
