Bell's Theorem: A New Perspective

Adán Cabello

A recent proof of Bell's theorem without inequalities [A. Cabello, Phys. Rev. Lett. 86, 1911 (2001)] is formulated as a Greenberger-Horne-Zeilinger-type proof involving just two observers. On one hand, this new approach allows us to derive an experimentally testable Bell inequality which is violated by quantum mechanics. On the other hand, it leads to a new state-independent proof of the Kochen-Specker theorem and provides a wider perspective on the relations between the major proofs of no hidden variables.

N. David Mermin

Two examples are given that substantially simplify the no-hidden-variables theorem of Kochen and Specker, greatly reducing the number of observables considered and requiring no intricate geometric argument. While one of the examples also obeys a more powerful version of Bell's theorem, the other does not. The examples provide a new perspective on both of these fundamental theorems and on the relation between them.

Maaneli Derakhshani

Michael L. Ulrey

A parameterized operational representation of an EPRB-like experiment is presented that facilitates direct comparisons among mathematical models that characterize the concepts of local hidden variables, the factorization condition, remote context independence, remote outcome independence, local causality, determinism, predictability, and quantum mechanics. The different models and conditions are derived from a common template, differentiated by parameter adjustment only. This perspective enables new and easier proofs of some existing results. It also clarifies the relationships among the various notions of locality and their relationship to the Bell-CHSH inequalities. Included are tables that make proofs short and intuitive, and figures that dramatize the differences between sets of correlations of quantum mechanics (QM) and those of realistic, local, deterministic, or predictable models. In addition, a novel proof of the no-communication theorem for QM provides a new perspective on why it is true.