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arXiv · 1903.06337

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

Lay Nam Chang·Djordje Minic·Tatsu Takeuchi
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Abstract

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.

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Lay Nam Chang, Djordje Minic, Tatsu Takeuchi. 2019-03-15. Spekkens' Toy Model, Finite Field Quantum Mechanics, and the Role of Linearity. https://doi.org/10.1088/1742-6596/1275/1/012036

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