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the quantum seems to allow fewer rounds in the interactive proof

This seems important. What if IP -> QIP is like O(N) -> O(log N)?




The result, IIRC, is that all of QIP can be done in three rounds, whereas if the same held in the classical world the polynomial hierarchy would collapse (which is considered about as likely as P=NP). Not of practical value, but it does point out that QIP is a slightly different beast than IP when you include the number of rounds.




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