Quantum protocols within Spekkens' toy model

The ZX calculus , Non - Locality and Spekkens toy theory

iii Acknowledgements v 1 Background 1 1.1 Process theories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 A bit of category theory . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.3 A distinction between classical and quantum systems . . . . . . . . . . 4 1.4 Particularly important maps . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.5 Spiders . . . . . . ....

Model checking quantum protocols

We introduce model-checking techniques for the automated analysis of quantum information protocols. These protocols take advantage of features of quantum theory such as entanglement and quantum measurement and some implementations already exist. Our techniques enable us to model a class of quantum protocols (those expressible within the stabilizer formalism) which are simulable in polynomial ti...

Depicting qudit quantum mechanics and mutually unbiased qudit theories

We generalize the ZX calculus to quantum systems of dimension higher than two. The resulting calculus is sound and universal for quantum mechanics. We define the notion of a mutually unbiased qudit theory and study two particular instances of these theories in detail: qudit stabilizer quantum mechanics and Spekkens-Schreiber toy theory for dits. The calculus allows us to analyze the structure o...

Toy Quantum Categories

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 v...

Quantum interference in thermoelectric molecular junctions: A toy model perspective