4
Two Queens

Well the answer isn't 3 and I've never seen a situation where it took more than 4 turns. Even in all cases with your own king in the way, I haven't seen it take more than 4 turns.
I'm not sure if my answer is correct but I recall reading about this before.
What is the maximum number of moves needed to checkmate a lone king with two queens? I think four.
http://chessskill.blogspot.com/2013/05/checkmate-with-two-queens.html