Imitating quantum probabilities: Beyond Bell's theorem and Tsirelson bounds

Abstract

Local hidden-variable model of singlet-state correlations discussed in M. Czachor, Arithmetic loophole in Bell's Theorem: Overlooked threat to entangled-state quantum cryptography, Acta Phys. Polon. A 139, 70-83 (2021), is shown to be a particular case of an infinite hierarchy of local hidden-variable models based on an infinite hierarchy of calculi. Violation of Bell-type inequalities is shown to be a `confusion of languages' problem, a result of mixing different but neighboring levels of the hierarchy. Mixing of non-neighboring levels results in violations beyond the Tsirelson bounds.

Version published online in Foundations of Science. A talk related to this paper can be watched at https://www.youtube.com/watch?v=W5z8HfIltO4

References in corpus (3)

• Unifying Aspects of Generalized Calculus
• Arithmetic loophole in Bell's theorem: An overlooked threat to entangled-state quantum cryptography
• Introduction to Projective Arithmetics

Cited by in corpus (2)

• Contra Bellum: Bell's theorem as a confusion of languages
• On the Relativity of Quantumness as Implied by Relativity of Arithmetic and Probability