  We study experimentally a system comprised of linear chains of spin-1/2
nuclei that provides a test-bed for multi-body dynamics and quantum information
processing. This system is a paradigm for a new class of quantum information
devices that can perform particular tasks even without universal control of the
whole quantum system. We investigate the extent of control achievable on the
system with current experimental apparatus and methods to gain information on
the system state, when full tomography is not possible and in any case highly
inefficient.
