Generalized Greenberger-Horne-Zeilinger arguments from quantum logical analysis

TL;DR

This paper reformulates GHZ arguments using quantum logic, analyzing how different states and contexts influence nonclassical correlations and the potential for GHZ-based quantum games.

Contribution

It introduces a generalized, operator-based GHZ framework within four nonintertwining contexts, expanding the understanding of quantum nonlocality and contextuality.

Findings

GHZ arguments can be recast in quantum logical terms

The performance depends on the choice of observables and states

Different GHZ games emerge depending on the state and context

Abstract

The Greenberger-Horne-Zeilinger (GHZ) argument against noncontextual local hidden variables is recast in quantum logical terms of fundamental propositions, states and probabilities. Unlike Kochen-Specker- and Hardy-like configurations, this operator based argument proceeds within four nonintertwining contexts. The nonclassical performance of the GHZ argument is due to the choice or filtering of observables with respect to a particular state. We study the varieties of GHZ games one could play in these four contexts, depending on the chosen state of the GHZ basis.