Graphical Calculus for Qutrit Systems

We introduce a graphical calculus for multi-qutrit systems (the qutrit ZX-calculus) based on the framework of dagger symmetric monoidal categories. This graphical calculus consists of generators for building diagrams and rules for transforming diagrams, which is obviously different from the qubit ZX-calculus. As an application of the qutrit ZX-calculus, we give a graphical description of a (2, 3) threshold quantum secret sharing scheme. In this way, we prove the correctness of the secret sharing scheme in a intuitively clear manner instead of complicated linear algebraic operations.