论文标题
希尔伯特空间效应代数的共存及其对称转换的表征
Coexistency on Hilbert space effect algebras and a characterisation of its symmetry transformations
论文作者
论文摘要
希尔伯特空间效应代数是一种基本的数学结构，用于描述路德维希（Ludwig）的量子力学制定中的分离量子测量。每个效果代表量子（模糊）事件。共存的关系在该理论中起着重要的作用，因为当可以通过应用合适的设备一起测量两个量子事件时，它表达了它。本文的第一个目标是回答一个关于这种关系的非常自然的问题，即，当两个效果与完全相同的效果共存时？另一个主要目的是描述效应代数与共存关系的所有自动形态。特别是，我们将看到它们与通常的标准自动形态有很大不同，例如在路德维希定理中出现。作为我们方法的副产品，我们还加强了Molnar定理。
The Hilbert space effect algebra is a fundamental mathematical structure which is used to describe unsharp quantum measurements in Ludwig's formulation of quantum mechanics. Each effect represents a quantum (fuzzy) event. The relation of coexistence plays an important role in this theory, as it expresses when two quantum events can be measured together by applying a suitable apparatus. This paper's first goal is to answer a very natural question about this relation, namely, when two effects are coexistent with exactly the same effects? The other main aim is to describe all automorphisms of the effect algebra with respect to the relation of coexistence. In particular, we will see that they can differ quite a lot from usual standard automorphisms, which appear for instance in Ludwig's theorem. As a byproduct of our methods we also strengthen a theorem of Molnar.
