  Many experiments in quantum information aim at creating multi-partite
entangled states. Quantifying the amount of entanglement that was actually
generated can, in principle, be accomplished using full-state tomography. This
method requires the determination of a parameter set that is growing
exponentially with the number of qubits and becomes infeasible even for
moderate numbers of particles. Non-trivial bounds on experimentally prepared
entanglement can however be obtained from partial information on the density
matrix. The fundamental question that needs to be addressed in this context is
then formulated as: What is the entanglement content of the least entangled
quantum state that is compatible with the available measurement data?
  We formulate the problem mathematically employing methods from the theory of
semi-definite programming and then address this problem for the case, where the
goal of the experiment is the creation of graph states. The observables that we
consider are the generators of the stabilizer group, thus the number of
measurement settings grows only linearly in the number of qubits. We provide
analytical solutions as well as numerical methods that may be applied directly
to experiments, and compare the obtained bounds with results from full-state
tomography for simulated data.
