Safer mechanisms of distributing and establishing "root" keys for identify verification (so you can then use them easier with normal D-H on normal internet) is one use case I recall from 1990s.
But few years ago I heard of some other interesting uses where quantum properties were used to essentially enable DWDM-like virtual circuit routing with higher capacity - though I would have to look again if it went anywhere or into scrap heap of quantum BS.
> Safer mechanisms of distributing and establishing "root" keys for identify verification
Except it doesn't solve the mitm problem, so its not really safer.