Operational Mermin non-locality and All-vs-Nothing arguments
This work addresses the need for secure quantum secret sharing algorithms by providing new resources based on contextuality, though it appears incremental as it builds on recent developments in operational Mermin non-locality.
The authors tackled the problem of identifying quantum realisable All-vs-Nothing models by leveraging operational Mermin non-locality arguments, resulting in a diverse family of maximally contextual models that lie on the faces of the no-signalling polytope with no local elements.
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 provide a large, novel family of quantum realisable All-vs-Nothing models. 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.