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Aug 11, 2016 at 22:42 comment added batconjurer Well, as I mentioned in the question, it's not hard to see that $D^2=I $ iff $D$ commutes with U. But any diagonal unitary satisfying $D^2=I $ can only have $\pm1$ on the diagonal and so is real.
Aug 11, 2016 at 16:11 history edited Josu Etxezarreta Martinez CC BY-SA 3.0
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Aug 11, 2016 at 15:25 history answered Josu Etxezarreta Martinez CC BY-SA 3.0