Manuscript Hawk01-B@1 · Hawk01-B.tex · lemma · cfa976f1

Lemma: Weyl twirl

Internally generated key and sequential logical transfer › Weyl operators and the first emission · lines 704–718 · proof included or linked

Hawk01-B@1#lem:twirl, Hawk01-B@1#eq:twirl

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For every $Y \in B (C^{d})$ ,

\frac{1}{d ^{2}} r \sum U_{r} Y U_{r}^{†} = Tr (Y) \frac{I _{d}}{d} .

Proof. Averaging over $b$ removes every off-diagonal matrix unit. Averaging over $a$ distributes each surviving diagonal entry uniformly over the computational basis.

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Hawk01-B@1#eq:twirl · line 707
$\frac{1}{d ^{2}} r \sum U_{r} Y U_{r}^{†} = Tr (Y) \frac{I _{d}}{d} .$

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section: Weyl operators and the first emission
section: Weyl operators and the first emission