Multi-setting Greenberger-Horne-Zeilinger Paradoxes

TL;DR

This paper develops a new class of GHZ paradoxes allowing multiple measurement settings per observer, demonstrating genuine n-partite nonlocality for arbitrary n-qubit GHZ states, including even numbers of qubits.

Contribution

It introduces a general construction for multi-setting GHZ paradoxes applicable to n-qubit states, filling a gap for even-numbered qubits and enhancing understanding of quantum nonlocality.

Findings

Constructed multi-setting GHZ paradoxes for arbitrary n-qubit states.

Established genuine n-partite nonlocality without subset paradoxes.

Addressed the absence of GHZ paradoxes for even-qubit GHZ states.

Abstract

Greenberger-Horne-Zeilinger (GHZ) paradox provides an all-versus-nothing test for the quantum nonlocality. In all the GHZ paradoxes known so far each observer is allowed to measure only two alternative observables. Here we shall present a general construction for GHZ paradoxes in which each observer measuring more than two observables given that the system is prepared in the $n$-qudit GHZ state. By doing so we are able to construct a multi-setting GHZ paradox for the $n$-qubit GHZ state, with $n$ being arbitrary, that is genuine $n$-partite, i.e., no GHZ paradox exists when restrict to a subset of number of observers for a given set of Mermin observables. Our result fills up the gap of the absence of a genuine GHZ paradox for the GHZ state of an even number of qubits, especially the four-qubit GHZ state as used in GHZ's original proposal.