  We present a renormalization scheme which simplifies the dynamics of an
important class of interacting multi-qubit systems. We show that a wide class
of M+1 qubit systems can be reduced to an equivalent n+1 qubit system with n
equal to, or greater than, 2, for any M. Our renormalization scheme faithfully
reproduces the overall dynamics of the original system including the
entanglement properties. In addition to its direct application to atom-cavity
and nanostructure systems, the formalism offers insight into a variety of
situations ranging from decoherence due to a spin-bath with its own internal
entanglement, through to energy transfer processes in organic systems such as
biological photosynthetic units.
