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 Moln\'ar.

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希尔伯特空间效应代数的共存及其对称变换的表征

希尔伯特空间效应代数是一种基本的数学结构，用于描述路德维希量子力学公式中的非清晰量子测量。每个效应代表一个量子（模糊）事件。共存关系在该理论中起着重要作用，因为它表达了何时可以通过应用合适的设备一起测量两个量子事件。本文的第一个目标是回答关于这种关系的一个非常自然的问题，即，当两种效果以完全相同的效果共存时？另一个主要目的是描述关于共存关系的效果代数的所有自同构。特别是，我们将看到它们与通常的标准自同构有很大不同，例如出现在路德维希定理中。