  The preparation of highly entangled many-body systems is one of the central
challenges of both basic and applied science. The complexity of interparticle
interaction and environment coupling increases rapidly with the number of
to-be-entangled subsystems, rendering the requirements on the control of
many-body quantum systems ever more restrictive. We propose an approach that
allows to derive optimal control Hamiltonians in a purely algebraic fashion.
These drive a composite quantum system rapidly into that highly entangled state
which can be created most efficiently for a given interaction mechanism, and
which bears entanglement that is robust against decoherence.
