Multipartite entangled quantum states in coupled optical parametric interactions: Density matrix and entropy characterization

We describe the normal ordering method (NOM) as a convinient way to obtaining explicit forms of the state vectors and density matrices of quantum states, usually generated in multiple coupled parametric optical processes. As a specific example, our method is demonstrated for the states, generated in three second-order parametric optical processes - one parametric down-conversion accompanied by two up-conversion processes. The application of the method allowed us to calculate the entropic characteristics of the multipartite quantum system.