Opps.. hang on. Is late. Might have misunderstood your equations. Both for that operator both the "+1" and "-1" eigenstates are magic states. One of them will be completely positive, but I can't see which right now.
Correction for the magic state bit below. Need to think about this more!https://twitter.com/earltcampbell/status/1158468208543842304 …
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