Is there a way to map QScreen to X11 display number on Linux?

We have a visualization software that renders large scenes using a single process that opens multiple windows on different X displays. Xinerama is disabled so that you can not move windows between X displays. I can query the available screens using QApplication::screens() and get a QScreen for each configured display. My problem is that all QScreens have identical parameters (displays are identical, so all resolutions are same and virtual desktop coordinates are same because of separate X displays) so I can't differentiate between them.

Is there any way to get X11 DISPLAY handle from QScreen so I could determine the relative positioning of QScreens?