Real world article
(written from a production point of view)
The Barbicon Theatre was a theater in London, mentioned in a letter included in a portion of the Picard family album prepared for Star Trek Generations but not seen on-screen.
The letter, from an individual known only as "KT", expressed her hope that Jean-Luc Picard would met her at this theater. She described the current season "as an interesting one with several newly-discovered Pinter works."
The reference would appear to be a misspelled reference to the well-known real Barbican theatre.