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In a previous article [1] we presented an argument to obtain (or ratherinfer) Born's rule, based on a simple set of axioms named "Contexts, Systemsand Modalities" (CSM). In this approach there is no "emergence", but thestructure of quantum mechanics can be attributed to an interplay between thequantized number of modalities that are accessible to a quantum system, and thecontinuum of contexts that are required to define these modalities. The stronglink of this derivation with Gleason's theorem was emphasized, with theargument that CSM provides a physical justification for Gleason's hypotheses.Here we extend this result by showing that an essential one among thesehypotheses - the need of unitary transforms to relate different contexts - canbe removed and is better seen as a necessary consequence of Uhlhorn's theorem.

Revisiting Born's rule through Uhlhorn's and Gleason's theorems