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Aug 2, 2012 at 2:53 comment added Terry Loring A technical point here: one needs to select $H$ with spectrum in $[0,2\pi)$ so that $\overline{H}$ has the same spectrum and we can conclude form the equality of exponentials the equality of $H$ and $\overline{H}$.
Jul 30, 2012 at 5:29 comment added Zhang Xiao Thanks a lot Suvrit! I find your answer quite simple and illuminating.
Jul 29, 2012 at 20:03 history answered Suvrit CC BY-SA 3.0