  In the usual tomography of multipartite entangled quantum states one assumes
that the measurement devices used in the laboratory are under perfect control
of the experimenter. In this paper, using the so-called SWAP concept introduced
recently, we show how one can remove this assumption in realistic experimental
conditions and nevertheless be able to characterize the produced multipartite
state based only on observed statistics. Such a black box tomography of quantum
states is termed self-testing. As a function of the magnitude of the Bell
violation, we are able to self-test emblematic multipartite quantum states such
as the three-qubit W state, the three- and four-qubit
Greenberger-Horne-Zeilinger states, and the four-qubit linear cluster state.
