Contexts, systems and modalities in Quantum physics

Alexia Auffèves, Philippe Grangier

Philippe Grangier

Alexia Auffèves, Philippe Grangier

In previous articles, we presented a derivation of Born’s rule and unitary transforms in Quantum Mechanics (QM), from a simple set of axioms built upon a physical phenomenology of quantization—physically, the structure of QM results of an interplay between the quantized number of “modalities” accessible to a quantum system, and the continuum of “contexts” required to define these modalities. In the present article, we provide a unified picture of quantum measurements within our approach, and justify further the role of the system–context dichotomy, and of quantum interferences. We also discuss links with stochastic quantum thermodynamics, and with algebraic quantum theory.

F. J. Burghardt

Andrei Yu. Khrennikov

Alexia Auffèves, Philippe Grangier

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.