Subspace controllability of multi-partite spin networks

In a network of spin 12 particles, controlled through an external electro-magnetic field, the gyromagnetic ratio each is parameter that characterizes interaction with control field. Multipartite networks are such spins divided into subsets according to their and in one set interact same way all another set. Due presence symmetries these types systems, underlying Hilbert state space splits invariant subspaces for dynamics. Subspace controllability verified if every unitary evolution can be generated by dynamics on subspaces. We give exact characterization, terms graph theoretic conditions, subspace multipartite quantum networks. This extends unifies previous results.