论文标题
一般概率理论中的中间决定论
Intermediate determinism in general probabilistic theories
论文作者
论文摘要
量子理论是不确定的，但不是完全。当系统处于纯状态时，它具有确定性的属性，称为实际特性。量子系统（以纯状态）的实际属性充分确定了找到具有其他属性的系统的概率。我们称此功能中间确定性。在至少三个方面，量子理论的中间决定论是通过其性质晶格的结构来保证的。这一观察结果来自格里森定理，这就是为什么它未能在第二维度中保持。在这项工作中，我们将中间确定论的想法从属性扩展到测量。在此扩展下，中间的确定论是从可分离的希尔伯特空间的量子效应的结构中遵循的任何维度，包括尺寸二。然后，我们发现普通概率理论遵守中间决定论的必要条件。我们表明，尽管相关，但无限制假设和格里森型定理既不必需，也不足以用于中间的决定论。
Quantum theory is indeterministic, but not completely so. When a system is in a pure state there are properties it possesses with certainty, known as actual properties. The actual properties of a quantum system (in a pure state) fully determine the probability of finding the system to have any other property. We call this feature intermediate determinism. In dimensions of at least three, the intermediate determinism of quantum theory is guaranteed by the structure of its lattice of properties. This observation follows from Gleason's theorem, which is why it fails to hold in dimension two. In this work we extend the idea of intermediate determinism from properties to measurements. Under this extension intermediate determinism follows from the structure of quantum effects for separable Hilbert spaces of any dimension, including dimension two. Then, we find necessary and sufficient conditions for a general probabilistic theory to obey intermediate determinism. We show that, although related, both the no-restriction hypothesis and a Gleason-type theorem are neither necessary nor sufficient for intermediate determinism.
