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 $logPhi$), can be identified and their cross-overs studied.
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