Depicting qudit quantum mechanics and mutually unbiased qudit theories

Understand

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 of qudit stabilizer quantum mechanics and provides a geometrical picture of qudit stabilizer theory using D-toruses, which generalizes the Bloch sphere picture for qubit stabilizer quantum mechanics.