Is contextuality about the identity of random variables?

Springer Verlag
Publication Type:
Journal Article
Foundations of Physics: an international journal devoted to the conceptual and fundamental theories of modern physics, biophysics, and cosmology, 2021, 51, (1), pp. 1-13
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Recent years have seen new general notions of contextuality emerge. Most of these employ context-independent symbols to represent random variables in different contexts. As an example, the operational theory of (Spekkens in Phys Rev A 71(5):52108, 2005) treats an observable being measured in two different contexts identically. Non-contextuality in this approach is the impossibility of drawing ontological distinctions between identical elements of the operational theory. However, a recent collection of work seeks to exploit context-dependent symbols of random variables to interpret contextuality (Kujala et al. in Phys Rev Lett 115(15):150401, 2015; Dzhafarov and Kujala in Phys Scr T163:014009, 2014). This approach associates contextuality with the possibility of imposing a particular joint distribution on random variables recorded under different experimental contexts. This paper compares these two different treatments of random variables and highlights the limitations of the context-dependent approach as a physical theory.
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