Qudit shift and phase operators
= Qudit shift and phase operators
{title2=$X|j\rangle=|j+1\rangle,\quad Z|j\rangle=\omega^j|j\rangle$}
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 $X^sZ^{-r}$ is $Z^rX^{-s}$, with the order reversed. These operators implement the receiver corrections in <qudit teleportation>.