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Spekkens' Toy Model, Finite Field Quantum Mechanics, and the Role of Linearity

Abstract

We map Spekkens' toy model to a quantum mechanics defined over the finite field F₅. This allows us to define arbitrary linear combinations of the epistemic states in the model. For Spekkens' elementary system with only 2²=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.

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