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Set of unitaries with "spread-like" properties
I'm interested in finding two sets of $N$ unitary $N \times N$ matrices $U_{1}, \ldots, U_{N}$, $V_{1}, \ldots, V_{N}$ such that:
$
\sup\limits_{X, Y}\sum\limits_{j,k = 1}^{N} |\mathrm{Tr}(YU_{j}XV_{...
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