“All-Versus-Nothing” Contextuality in Graph States

Abstract

In this chapter I introduce a unified construction of Greenberger–Horne–Zeilinger (GHZ)-type paradoxes for graph states, providing insights into the contradictions between classical theory and quantum mechanics. While GHZ-type paradoxes have been extensively studied across various systems, their full range of applicability remains unknown, and a unified framework has yet to be discovered. By demonstrating that GHZ-type paradoxes extend beyond graph states, we broaden the understanding of their existence. Additionally, the presented results have significant implications for quantum state verification in graph states, entanglement detection, and the development of GHZ-type steering paradoxes for mixed states. Through a photonic experiment, we verify the GHZ-type paradoxes by measuring the success probability of their corresponding perfect Hardy-type paradoxes and showcase their practical applications. This research enriches our comprehension of quantum paradoxes within the field of quantum foundations and holds potential for a wide range of quantum information tasks.