  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. We also use our
framework to describe generalizations of Spekkens toy theory to higher
dimensional systems. This gives a novel proof that qudit stabilizer quantum
mechanics and Spekkens-Schreiber toy theory for dits are operationally
equivalent in three dimensions. The qudit pictorial calculus is a useful tool
to study quantum foundations, understand the relationship between qubit and
qudit quantum mechanics, and provide a novel, high level description of quantum
information protocols.
