  Integrated Information Theory (IIT) has emerged as one of the leading
research lines in computational neuroscience to provide a mechanistic and
mathematically well-defined description of the neural correlates of
consciousness. Integrated Information ($\Phi$) quantifies how much the
integrated cause/effect structure of the global neural network fails to be
accounted for by any partitioned version of it. The holistic IIT approach is in
principle applicable to any information-processing dynamical network regardless
of its interpretation in the context of consciousness. In this paper we take
the first steps towards a formulation of a general and consistent version of
IIT for interacting networks of quantum systems. A variety of different phases,
from the dis-integrated ($\Phi=0$) to the holistic one (extensive $\log\Phi$),
can be identified and their cross-overs studied.
