Spekkens' Toy Model, Finite Field Quantum Mechanics, and the Role of Linearity
Lay Nam Chang, Djordje Minic, and Tatsu Takeuchi
TL;DR
This paper maps Spekkens' toy model to finite field quantum mechanics, enabling linear combinations of states and revealing both agreements and differences in entanglement properties.
Contribution
It introduces a finite field quantum framework for Spekkens' model, highlighting new linear structure and entanglement distinctions.
Findings
Exact mapping for single elementary systems
Linear combinations of states are well-defined in the mapped model
Differences in entangled states between the models for two systems
Abstract
We map Spekkens' toy model to a quantum mechanics defined over the finite field . This allows us to define arbitrary linear combinations of the epistemic states in the model. For Spekkens' elementary system with only 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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