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.