  Multipartite entanglement is very poorly understood despite all the
theoretical and experimental advances of the last decades. Preparation,
manipulation and identification of this resource is crucial for both practical
and fundamental reasons. However, the difficulty in the practical manipulation
and the complexity of the data generated by measurements on these systems
increase rapidly with the number of parties. Therefore, we would like to
experimentally address the problem of how much information about multipartite
entanglement we can access with incomplete measurements. In particular, it was
shown that some types of pure multipartite entangled states can be witnessed
without measuring the correlations [M. Walter et al., Science 340, 1205 (2013)]
between parties, which is strongly demanding experimentally. We explore this
method using an optical setup that permits the preparation and the complete
tomographic reconstruction of many inequivalent classes of three- and
four-partite entangled states, and compare complete versus incomplete
information. We show that the method is useful in practice, even for non-pure
states or non ideal measurement conditions.
