Toy quantum categories

Details Toy quantum categories Toy quantum categories

2008-08-07

arxiv.org/abs/0808.1037v1

Physics

Quantum Physics

11 pages and 8 pictures. In the proceedings of Quantum Physics and Logic 2008, Electronic Notes in theoretical Computer Scienc

Scientific paper

We show that Rob Spekken's toy quantum theory arises as an instance of our categorical approach to quantum axiomatics, as a (proper) subcategory of the dagger compact category FRel of finite sets and relations with the cartesian product as tensor, where observables correspond to dagger Frobenius algebras. This in particular implies that the quantum-like properties of the toy model are in fact very general category-theoretic properties. We also show the remarkable fact that we can already interpret complementary quantum observables on the two-element set FRel.

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