Multi-setting Greenberger-Horne-Zeilinger theorem

TL;DR

This paper generalizes the GHZ theorem to include multiple measurement settings per party for odd-numbered multi-party systems, expanding the understanding of quantum nonlocality and potential applications like secret sharing.

Contribution

It introduces a generalized GHZ theorem involving multiple settings per party, applicable to systems with more than two settings and odd numbers of parties, extending previous results.

Findings

Generalized GHZ theorem for multiple settings per party

Applicable to odd-numbered multi-party systems

Potential applications in quantum secret sharing

Abstract

We present a generalized Greenberger-Horne-Zeilinger (GHZ) theorem, which involves more than two local measurement settings for some parties, and cannot be reduced to one with less settings. Our results hold for an odd number of parties. We use a set of observables, which are incompatible but share a common eigenstate, here a GHZ state. Such observables are called concurrent. The idea is illustrated with an example of a three-qutrit system and then generalized to systems of higher dimensions, and more parties. The GHZ paradoxes can lead to, e.g., secret sharing protocols.