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Article

Revisiting Born’s Rule through Uhlhorn’s and Gleason’s Theorems

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Institut Néel, 25 rue des Martyrs, BP166, CEDEX 9, F38042 Grenoble, France
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Laboratoire Charles Fabry, Institut d’Optique Graduate School, Centre National de la Recherche Scientifique (CNRS), Université Paris Saclay, F91127 Palaiseau, France
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Author to whom correspondence should be addressed.
Academic Editors: Ronnie Kosloff, Raymond Laflamme, Juan Pablo Paz, Michael Zwolak and Sebastian Deffner
Entropy 2022, 24(2), 199; https://doi.org/10.3390/e24020199
Received: 7 December 2021 / Revised: 20 January 2022 / Accepted: 26 January 2022 / Published: 28 January 2022
(This article belongs to the Special Issue Quantum Darwinism and Friends)
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. View Full-Text
Keywords: quantum mechanics; contextuality; Gleason’s theorem; Uhlhorn’s theorem quantum mechanics; contextuality; Gleason’s theorem; Uhlhorn’s theorem
MDPI and ACS Style

Auffèves, A.; Grangier, P. Revisiting Born’s Rule through Uhlhorn’s and Gleason’s Theorems. Entropy 2022, 24, 199. https://doi.org/10.3390/e24020199

AMA Style

Auffèves A, Grangier P. Revisiting Born’s Rule through Uhlhorn’s and Gleason’s Theorems. Entropy. 2022; 24(2):199. https://doi.org/10.3390/e24020199

Chicago/Turabian Style

Auffèves, Alexia, and Philippe Grangier. 2022. "Revisiting Born’s Rule through Uhlhorn’s and Gleason’s Theorems" Entropy 24, no. 2: 199. https://doi.org/10.3390/e24020199

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