Qudit shift and phase operators ($X|j⟩=|j+1⟩,Z|j⟩={\omega }^j|j⟩$)

For an $n$-level qudit and primitive root of unity $\omega$, these unitary operators obey $X^n=Z^n=I$ and $ZX=\omega XZ$. The inverse of $X^s{Z}^{-r}$ is $Z^r{X}^{-s}$, with the order reversed. These operators implement the receiver corrections in qudit teleportation.