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... octonionic example as physical models.2 Working in a framework in which a physical system is described by specifying a set of basic observables and a finite-dimensional compact, convex set of states =-=[3, 30]-=-, I propose four axioms that, taken together, may be glossed as saying that (i) a system appears completely classical as restricted to any single basic observable, (ii) all basic observables are equiv...

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...lly bi-symmetric. If A is bi-symmetric, then G acts transitively. Clearly, the quantum model discussed above is fully bi-symmetric. Bi-symmetry and full bi-symmetry, are very natural conditions. (See =-=[17]-=- for further discussion and motivation of the latter.) Definition. A SPIN form1 for the model A is a real bilinear form B on E(A) that is symmetric, positive in the sense that B(a,b) ≥ 0 for all a,b ∈...

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...rmation theoretic quantities like entropy [20, 156], general no-cloning and no-broadcasting theorems [21, 22], steering [25], teleportation [23], correlations between systems [24, 104, 139], symmetry =-=[179]-=-, theories with purifications [45], and state discrimination [111, 109]. There have also been many other studies with a similar theme, but not within the general probabilistic theories framework, such...

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...lly bi-symmetric. If A is bi-symmetric, then G acts transitively. Clearly, the quantum model discussed above is fully bi-symmetric. Bi-symmetry and full bi-symmetry, are very natural conditions. (See =-=[17]-=- for further discussion and motivation of the latter.) Definition. A SPIN form1 for the model A is a real bilinear form B on E(A) that is symmetric, positive in the sense that B(a,b) ≥ 0 for all a,b ∈...

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... every outcome x ∈ X (A), there 4Thanks to Jon Barrett for pointing out this sort of simple example. 7 exists a unique state α ∈ E∗(A) with α(x) = 1. If A is state-complete (as was tacitly assumed in =-=[28]-=-), this coincides with the oresent notion. Sharpness (in one form or another) has a long history in the quantum-logical literature. In particular, it played a central role in Gunson’s axiomatics for q...