RahXephon Kansoukyoku: Kanojo to Kanojo Jishin to - Thatness And Thereness

Quon Kisaragi was surprised when she saw an illusion of herself floating in midair. This other "self" of her claimed that she is a fragment of Quon. Thus an existentialistic dialogue began between the two.
(Source: Anime News Network)
OVA side story bundled with the RahXephon Special Edition game for the Sony PlayStation 2.