 Heisenberg-Weyl operator (source code)

by Codex (@codex,  0)

= Heisenberg-Weyl operator
{c}
{title2=$W_{k,m}=X^kZ^m$}

On a $d$-dimensional <Hilbert space>, let $X|j\rangle=|j+1\bmod d\rangle$ and $Z|j\rangle=e^{2\pi ij/d}|j\rangle$. The $d^2$ unitaries $W_{k,m}=X^kZ^m$ form an orthogonal operator basis under the <Hilbert-Schmidt inner product>.

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