How would I detect pressing one of the arrow keys in qt?
Handling the key click event in the top most widget in the hierarchy. See list of key codes , Qt :: Left - Qt :: Down range is what you are interested in.
Also, will the application still detect them if minimized?
No. He would only find them if he had keyboard focus, and this is not the case when it is minimized. You cannot configure global hotkeys in a cross-platform manner in Qt.