Alladi Ramakrishnan Hall

Contextuality beyond the Kochen-Specker theorem

Ravi Kunjwal

IMSc

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 are physically identical. We call such a hypothesis "noncontextuality", an instance of Leibniz's principle of the identity of indiscernibles. The results I will present concern the failure of this hypothesis -- a failure we call "contextuality" -- when one tries to embed an operational theory (such as quantum theory) in the framework of an ontological model. The Kochen-Specker theorem demonstrates the failure of noncontextuality for deterministic ontological models of quantum theory. We will go beyond the Kochen-Specker theorem by asking what operational facts must be verified in experiments to conclude that Nature does not admit noncontextual models, not even indeterministic ones. This is part of the larger project of delineating the exact operational features of quantum theory (and indeed, any putative "post-quantum" theories) that set it apart from a classical probabilistic theory and power its computational or information-theoretic advantages.