Spekkens' Toy Model, Finite Field Quantum Mechanics, and the Role of Linearity. (arXiv:1903.06337v1 [quant-ph])

We map Spekkens' toy model to a quantum mechanics defined over the finite
field $\mathbb{F}_5$. This allows us to define arbitrary linear combinations of
the epistemic states in the model. For Spekkens' elementary system with only
$2^2=4$ ontic states, the mapping is exact and the two models agree completely.
However, for a pair of elementary systems there exist interesting differences
between the entangled states of the two models.