Combinatorial approach to multipartite quantum systems : basic formulation

In this paper we give a method to associate a graph with an arbitrary density matrix referred to a standard orthonormal basis in the Hilbert space of a finite dimensional quantum system. We study the related issues like classification of pure and mixed states, Von-Neumann entropy, separability of multipartite quantum states and quantum operations in terms of the graphs associated with quantum states. In particular, we give a necessary and sufficient criterion for a m-partite quantum state to be separable.