From breakfast, lunch, and dinner to the Bell-inequality tetrahedron
Abstract
A simple pedagogical discussion and visualization of certain Bell inequalities is presented with the help of a system involving two \textquotedblleft twins\textquotedblright, originally discussed in 2605.03104. These twins answer identically when the same `question' is posed, here exemplified with: Did you like breakfast/lunch/dinner? In analogy, for two entangled particles at distant locations, the `twin-like' quantum state is such that the same outcome for the same measurement (i.e. spin direction) is obtained. In the space (X,Y,Z) of mixed moments (i.e. X refers to breakfast-lunch correlation, being $1$ for same answers and −1 for opposite ones), the space of Bell local models is contained in a tetrahedron, while the quantum space is bound by an elliptope that embeds the tetrahedron. The whole no-signalling region in the (X,Y,Z) space is the cube [−1,1]3. The twin scenario applies e.g. to the decay of the Higgs into fermions.
Related
- No violation on a generalisation of Leggett-Garg inequality and Bell-CHSH inequality with extended probability
- Bell-inequality violation in light transmitted through disordered emitter ensembles
- Bell inequality violation with momentum-entangled massive particles
- Violation of Bell-type Inequality in the Hanbury Brown-Twiss (HBT) Toy-Model: Quantum Correlations beyond Local-Realism
- The I3322 Bell inequality requires infinite dimensions
BibTeX
@misc{giacosa2026from,
title = {{From breakfast, lunch, and dinner to the Bell-inequality tetrahedron}},
author = {Francesco Giacosa},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.14436},
eprint = {2609.14436},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.14436},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - From breakfast, lunch, and dinner to the Bell-inequality tetrahedron
AU - Francesco Giacosa
PY - 2026
DA - 2026/09/13
PB - arXiv
DO - 10.48550/arxiv.2609.14436
UR - https://arxiv.org/abs/2609.14436
AB - A simple pedagogical discussion and visualization of certain Bell inequalities is presented with the help of a system involving two \textquotedblleft twins\textquotedblright, originally discussed in 2605.03104. These twins answer identically when the same `question' is posed, here exemplified with: Did you like breakfast/lunch/dinner? In analogy, for two entangled particles at distant locations, the `twin-like' quantum state is such that the same outcome for the same measurement (i.e. spin direction) is obtained. In the space (X,Y,Z) of mixed moments (i.e. X refers to breakfast-lunch correlation, being $1$ for same answers and −1 for opposite ones), the space of Bell local models is contained in a tetrahedron, while the quantum space is bound by an elliptope that embeds the tetrahedron. The whole no-signalling region in the (X,Y,Z) space is the cube [−1,1]^3. The twin scenario applies e.g. to the decay of the Higgs into fermions.
ER -