Bell’s theorem without inequalities: on the inception and scope of the GHZ theorem

Olival Freire Jr. and Osvaldo Pessoa Jr.

Submitted to “Quantum Nonlocality and Reality – 50 Years of Bell’s theorem”

Since its inception, fifty years ago, Bell’s theorem has had a long history not only of experimental tests but also of theoretical developments. Studying pairs of correlated quantum-mechanical particles separated in space, in a composite “entangled” state, Bell (1964) showed that the joint ascription of hidden-variables and locality to the system led to an inequality that is violated by the predictions of quantum mechanics. Fifteen years later, experiments confirmed the predictions of quantum mechanics, ruling out a large class of local realist theories.

One of the most meaningful theoretical developments that followed Bell’s work was the Greenberger-Horne-Zeilinger (GHZ) theorem, also known as Bell’s theorem without inequalities. In 1989, the American physicists Daniel Greenberger and Michael Horne, who had been working on Bell’s theorem since the late 1960s, together with Austrian physicist Anton Zeilinger, introduced a novelty to the testing of entanglement, extending Bell’s theorem in a different and interesting direction. Full text

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