This paper is an attempt to give a Quantum theory of Mathematical integrated information theory which is mathematical version of integrated information theory by Masafumi Oizumi, Larissa Albantakis, Giulio Tononi [2]. Using the definitions of Classical Mathematical Integrated Information Theory [1]. And considering that the Quantum theory is given by the functor which maps from a category whose objects is topology to a linear category whose objects are Hilbert spaces indexed with the objects from previous category. Also, we will be using the definition of conditional density matrix to define repertoire. We will be also discussing the relationship between consciousness and entanglement.