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

TL;DR

This paper introduces a new family of quantum models based on operational Mermin non-locality arguments, highlighting their maximal contextuality and potential for secure quantum secret sharing.

Contribution

It demonstrates that operational Mermin non-locality provides a broad, novel class of quantum All-vs-Nothing models with applications in quantum security.

Findings

Large family of quantum realizable All-vs-Nothing models

Models are maximally contextual and lie on the faces of the no-signalling polytope

Potential use in secure quantum secret sharing

Abstract

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.