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

Marek Czachor; Kamil Nalikowski

doi:10.1007/s10699-022-09856-y

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

Marek Czachor, Kamil Nalikowski

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3 Citations (Scopus)

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Abstract

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 language	English
Pages (from-to)	281-305
Number of pages	25
Journal	Foundations of Science
Volume	29
DOIs	https://doi.org/10.1007/s10699-022-09856-y
Publication status	Published - 2024

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

Keywords

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

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10.1007/s10699-022-09856-y

94766333Accepted author manuscript, 480 KBLicence: Other

Cite this

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abstract = "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 {\textquoteleft}confusion of languages{\textquoteright} problem, a result of mixing different but neighboring levels of the hierarchy. Mixing of non-neighboring levels results in violations beyond the Tsirelson bounds.",

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

Abstract

Bibliographical note

Keywords

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