Auffèves Alexia, Grangier Philippe
Institut Néel, 25 rue des Martyrs, BP166, CEDEX 9, F38042 Grenoble, France.
Laboratoire Charles Fabry, Institut d'Optique Graduate School, Centre National de la Recherche Scientifique (CNRS), Université Paris Saclay, F91127 Palaiseau, France.
Entropy (Basel). 2022 Jan 28;24(2):199. doi: 10.3390/e24020199.
In a previous article we presented an argument to obtain (or rather infer) Born's rule, based on a simple set of axioms named "Contexts, Systems and Modalities" (CSM). In this approach, there is no "emergence", but the structure of quantum mechanics can be attributed to an interplay between the quantized number of modalities that is accessible to a quantum system and the continuum of contexts that are required to define these modalities. The strong link of this derivation with Gleason's theorem was emphasized, with the argument that CSM provides a physical justification for Gleason's hypotheses. Here, we extend this result by showing that an essential one among these hypotheses-the need of unitary transforms to relate different contexts-can be removed and is better seen as a necessary consequence of Uhlhorn's theorem.
在之前的一篇文章中，我们基于一组名为“情境、系统与模态”（CSM）的简单公理，提出了一个获取（或者更确切地说是推断）玻恩规则的论证。在这种方法中，不存在“涌现”，但量子力学的结构可归因于量子系统可及的模态数量的量子化与定义这些模态所需的连续情境之间的相互作用。我们强调了此推导与格莱森定理的紧密联系，认为CSM为格莱森的假设提供了物理依据。在此，我们扩展了这一结果，表明这些假设中的一个关键假设——关联不同情境需要酉变换——可以被去除，并且最好将其视为乌尔曼定理的必然结果。
