Contextuality without incompatibility

Google meet: https://meet.google.com/upw-ynon-pkx

Abstract

Incompatibility of measurements is often considered to be a feature of a scenario which is essential to witnessing nonclassicality. Indeed, this most definitely is the case for Bell nonlocality (where we require both parties to have a set of incompatible measurements in order to violate a Bell inequality) and Kochen Specker contextuality (where in fact incompatibility is central to the very definition of the scenarios that are considered). Moreover, in  [Phys. Rev. Research 2, 013011 (2020)] it is claimed that measurement incompatibility is necessary and sufficient for operational contextuality. It was therefore something of a surprise to coauthors and I when we discovered a scenario in which we had no incompatibility but still had generalised contextuality [arXiv:2106.09045]. Developing an understanding of exactly how and why this works is the topic of [arXiv:2112.04521] based in a new convex-geometric framework for generalised contextuality [arXiv:1911.10386]. In this seminar I will try to explain this new convex-geometric framework and convey our understanding of exactly why incompatibility is neither necessary nor sufficient for witnessing generalised contextuality.