A mathematical framework for operational fine tunings

In the framework of ontological models, the features of quantum mechanics that emerge as inherently nonclassical always involve properties that are fine tuned, i.e. properties that hold at the operational level but break at the ontological level (they only hold for fine tuned values of the ontic parameters). Famous examples of such features are contextuality and nonlocality. We here develop a precise theory-independent mathematical framework for characterizing operational fine tunings. These are distinct from causal fine tunings - already introduced by Wood and Spekkens in [NJP,17 033002(2015)] - as they do not involve any assumption on the underlying causal structure. We show how all the already known examples of operational fine tunings fit into our framework, we discuss possibly new fine tunings and we use the framework to shed new light on the relation between nonlocality and generalized contextuality, where the former can involve a causal fine tuning too, unlike the latter. The framework is also formulated in the language of category theory and functors.

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This work was supported (in part) by the Fetzer Franklin Fund of the John E. Fetzer Memorial Trust.