  Entanglement witnesses provide tools to detect entanglement in experimental
situations without the need of having full tomographic knowledge about the
state. If one estimates in an experiment an expectation value smaller than
zero, one can directly infer that the state has been entangled, or specifically
multi-partite entangled, in the first place. In this article, we emphasize that
all these tests - based on the very same data - give rise to quantitative
estimates in terms of entanglement measures: "If a test is strongly violated,
one can also infer that the state was quantitatively very much entangled". We
consider various measures of entanglement, including the negativity, the
entanglement of formation, and the robustness of entanglement, in the bipartite
and multipartite setting. As examples, we discuss several experiments in the
context of quantum state preparation that have recently been performed.
