The idea of a player Quater-backing a powerplay ususally refers to a defenseman with a big shot and good passing skills along the blue line. They sort of control the power play, choosing to let a big shot go, or to pass it, a little like a football QB. They usually roam the blue line.
It's not always a defenseman, but almost always. Most of the time it's an offensive defenseman, often with a bit shot, ie. Shea Weber, Zdeno Chara, etc. Occasionally some forwards might play the role of a QB on the powerplay, but it doesn't happen as often.
Edler is about the closest we have to a powerplay QB.