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Chinese Physics Letters

“All versus Nothing” Inseparability for 2n Observers

梁林梅, 李承祖

Published Jan 1, 2003• 0 citations
OpenAlex

Abstract

We present an “all versus nothing” to show Bell's theorem without inequalities involving 2n observers. As a by-product, we also shows that quantum mechanics can violate Bell's inequality by a constant instead of by an amount that grows exponentially with 2n.

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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.
We introduce a two-observer all-versus-nothing proof of Bell's theorem which reduces the number of required quantum predictions from 9 [A. Cabello, Phys. Rev. Lett. 87, 010403 (2001); Z.-B. Chen et al., Phys. Rev. Lett. 90, 160408 (2003)] to 4, provides a greater amount of evidence against local realism, reduces the detection efficiency requirements for a conclusive experimental test of Bell's theorem, and leads to a Bell inequality which resembles Mermin's inequality for three observers [N. D. Mermin, Phys. Rev. Lett. 65, 1838 (1990)] but requires only two observers.
Abstract The all-versus-nothing proof of Bell nonlocality is a prominent demonstration of Bell’s theorem without inequalities. There are two kinds of such proofs: the deterministic all-versus-nothing proof and the probabilistic all-versus-nothing proof, which have received extensive research attention. Traditionally, all previous deterministic all-versus-nothing proofs are constructed based on stabilizer states. However, this work presents new deterministic proofs derived from non-stabilizer states, thereby breaking away from this conventional approach. These novel results not only significantly broaden the range of demonstrations of Bell nonlocality without inequalities but also offer valuable resources for certain quantum information processing applications.