Multi-setting Greenberger-Horne-Zeilinger Paradoxes

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.

5 pages, 0 figures

References in corpus (6)

• Experimental non-classicality of an indivisible quantum system
• State-independent experimental tests of quantum contextuality in a three dimensional system
• Greenberger-Horne-Zeilinger paradoxes from qudit graph states
• Greenberger-Horne-Zeilinger Nonlocality in Arbitrary Even Dimensions
• Rotational covariance and GHZ contradictions for three or more particles of any dimension
• Multi-setting Greenberger-Horne-Zeilinger theorem

Cited by in corpus (5)

• Advances in High Dimensional Quantum Entanglement
• Experimental GHZ Entanglement beyond Qubits
• Quantum Indistinguishability by Path Identity: The awakening of a sleeping beauty
• Experimental Test of Irreducible Four-Qubit Greenberger-Horne-Zeilinger Paradox
• Deterministic all-versus-nothing proofs of Bell nonlocality based on non-stabilizer states