Contextuality beyond the Kochen-Specker theorem

Understand

When it isn't possible to tell two distinct experimental procedures apart purely from their input/output statistics, then it seems a plausible hypothesis that the two procedures must be physically identical.

• We call such a hypothesis "noncontextuality", an instance of Leibniz's principle of the identity of indiscernibles.
• Read in the contrapositive, this hypothesis entails that any physical distinctions between two experimental procedures must necessarily lead to a difference in their operational statistics.
• The results I present in this thesis concern the failure of this hypothesis -- a failure dubbed "contextuality" -- when one tries to embed an operational theory (such as quantum theory) in the ontological models framework.