Imitating Quantum Probabilities: Beyond Bell's Theorem and Tsirelson Bounds

Marek Czachor, Kamil Nalikowski

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


Local hidden-variable model of singlet-state correlations discussed in Czachor (Acta Phys Polon A 139:70, 2021a) 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 can be interpreted as 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.

Original languageEnglish
Pages (from-to)281-305
Number of pages25
JournalFoundations of Science
Publication statusE-pub ahead of print - 13 Jul 2022

Bibliographical note

Funding Information:
Calculations were carried out at the Academic Computer Center in Gdańsk. The work was supported by the CI TASK grant ‘Non-Newtonian calculus with interdisciplinary applications’. KN has been supported by Ministry of Education and Science student fellowship ‘Szkoła Orłów’.

Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Nature B.V.

Copyright 2022 Elsevier B.V., All rights reserved.


  • Non-Diophantine arithmetic
  • Non-Newtonian calculus
  • Hidden variables
  • Bell inequality
  • Quantum cryptography
  • Hacking


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