  The existence of higher than pairwise quantum interference in the set-up, in
which there are more than two slits, is currently under experimental
investigation. However, it is still unclear what the confirmation of existence
of such interference would mean for quantum theory -- whether that usual
quantum mechanics is merely a limiting case of some more general theory or
whether that some assumption of quantum theory taken as a fundamental one does
not actually hold true. The present paper tries to understand why quantum
theory is limited only to a certain kind of interference.
