Greenberger-Horne-Zeilinger paradoxes from qudit graph states

TL;DR

This paper introduces a method to construct Greenberger-Horne-Zeilinger (GHZ) paradoxes for any number of particles using qudit graph states on GHZ graphs, extending the scope of quantum nonlocality tests.

Contribution

It presents a novel construction of GHZ paradoxes for arbitrary multipartite systems with qudits, expanding the understanding of quantum nonlocality beyond odd-numbered particle systems.

Findings

Derived a Bell inequality with maximal violation using graph states.

Established a state-independent Kochen-Specker inequality for quantum contextuality.

Extended GHZ paradoxes to systems with any number of particles.

Abstract

One fascinating way of revealing the quantum nonlocality is the all-versus-nothing test due to Greenberger, Horne, and Zeilinger (GHZ) known as GHZ paradox. So far genuine multipartite and multilevel GHZ paradoxes are known to exist only in systems containing an odd number of particles. Here we shall construct GHZ paradoxes for an arbitrary number (greater than 3) of particles with the help of qudit graph states on a special kind of graphs, called as GHZ graphs. Based on the GHZ paradox arising from a GHZ graph, we derive a Bell inequality with two $d$-outcome observables for each observer, whose maximal violation attained by the corresponding graph state, and a Kochen-Specker inequality testing the quantum contextuality in a state-independent fashion.