Operational Mermin non-locality and All-vs-Nothing arguments

Contextuality is a key resource in quantum information and the device-independent security of quantum algorithms. In this work, we show that the recently developed, operational Mermin non-locality arguments of [9] provide a large, novel family of quantum realisable All-vs-Nothing models [1]. In particular, they result in a diverse wealth of quantum realisable models which are maximally contextual (i.e. lie on the faces of the no-signalling polytope with no local elements), and could be used as a resource for the security of a new class of quantum secret sharing algorithms.