  We systematically investigate scrambling (or delocalizing) processes of
quantum information encoded in quantum many-body systems by using numerical
exact diagonalization. As a measure of scrambling, we adopt the tripartite
mutual information (TMI) that becomes negative when quantum information is
delocalized. We clarify that scrambling is an independent property of
integrability of Hamiltonians; TMI can be negative or positive for both
integrable and non-integrable systems. This implies that scrambling is a
separate concept from conventional quantum chaos characterized by
non-integrability. Furthermore, we calculate TMI in disordered systems such as
many-body localized (MBL) systems and the Sachdev-Ye-Kitaev (SYK) model. We
find that scrambling occurs but is slow in a MBL phase, while disorder in the
SYK model does not make scrambling slower but makes it smoother.
