  The ZX-Calculus is a graphical language for quantum mechanics. An
axiomatisation has recently been proven to be complete for an approximatively
universal fragment of quantum mechanics, the so-called Clifford+T fragment. We
focus here on the expressive power of this axiomatisation beyond Clifford+T
Quantum mechanics. We consider the full pure qubit quantum mechanics, and
mainly prove two results: (i) First, the axiomatisation for Clifford+T quantum
mechanics is also complete for all equations involving some kind of linear
diagrams. The linearity of the diagrams reflects the phase group structure, an
essential feature of the ZX-calculus. In particular all the axioms of the
ZX-calculus are involving linear diagrams. (ii) We also show that the
axiomatisation for Clifford+T is not complete in general but can be completed
by adding a single (non linear) axiom, providing a simpler axiomatisation of
the ZX-calculus for pure quantum mechanics than the one recently introduced by
Ng&Wang.
