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Distribution monads, contexuality, and cohomology

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If you have a question about this talk, please contact Uday Reddy.

In this talk, I will introduce distribution monads and will show how they can be exploited to give distributions on the set of measurement events. We’ll see how this construction naturally leads to the notion of presheaves on measurement contexts. Furthermore, a precise sheaf-theoretical definition of contexuality will be presented. Using Cech cohomology, we see a cohomological characterisation of contexuality. More precisely, we look at zeroth cohomology group to find a sufficient condition for contexuality. Also, contexuality in some well-known examples such as Bell Model, PR-box , and Hardy model from quantum mechanics will be analysed through this approach.

Finally, time permits, I will show how one can simultaneously have no-signaling models and hidden-variable theory (corresponding to non-contextual deterministic predictions of measurement outcomes) with the heavy use of signed probability measures (aka negative probabilities) based on a very recent work of Abramsky, Brandenburger, and Savochkin.

This talk is part of the Lab Lunch series.

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