Toy quantum categories (extended abstract)
<p>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 <strong>FRel</strong> of finite sets and relations with the cartesian product as tensor, where obs...
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| Format: | Journal article |
| Language: | English |
| Published: |
2011
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| Subjects: |
| Summary: | <p>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 <strong>FRel</strong> 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 categorytheoretic properties. We also show the remarkable fact that we can already interpret complementary quantum observables on the two-element set in <strong>FRel</strong>.</p> |
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