From this picture we can make out Tama, Ulith, and Mayu. The way Tama’s and Ulith’s hands are position makes me think that they are holding cards. And being a card game anime, I’m guessing they are playing an early form of WIXOSS. And we know that at some point Tama and Mayu were quite close.
My theory is that some sort of trauma happen to these three that caused them to make a wish. Tama wished to forget the experience and by extension her entire memory. While Mayu’s wish was to escape from everything and ended up sealing herself in that white room away from everything. As for Ulith; as she’s a sadist I’m think she is a lair Mayu talked about in episode 3 and probably caused that trauma.