Imitating quantum probabilities: Beyond Bell's theorem and Tsirelson bounds
arXiv:2105.12728 · doi:10.1007/s10699-022-09856-y
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.
arXiv commentVersion 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 (17)
- Quantum Cryptography
- Quantum Hacking: Experimental demonstration of time-shift attack against practical quantum key distribution systems
- Experimentally faking the violation of Bell's inequalities
- Waves along fractal coastlines: From fractal arithmetic to wave equations
- Relativity of arithmetic as a fundamental symmetry of physics
- On classical models of spin
- Towards a Coherent Theory of Physics and Mathematics: The Theory-Experiment Connection
- Unifying Aspects of Generalized Calculus
- Arithmetic loophole in Bell's theorem: An overlooked threat to entangled-state quantum cryptography
- Introduction to Projective Arithmetics
- Fourier transforms on Cantor sets: A study in non-Diophantine arithmetic and calculus
- Crystallization of space: Space-time fractals from fractal arithmetic
- Non-Newtonian mathematics instead of non-Newtonian physics: Dark matter and dark energy from a mismatch of arithmetics
- A loophole of all `loophole-free' Bell-type theorems
- Towards a Coherent Theory of Physics and Mathematics
- Simple fractal calculus from fractal arithmetic
- Entangled-state cryptographic protocol that remains secure even if nonlocal hidden variables exist and can be measured with arbitrary precision