All pure multipartite entangled states of qubits can be self-tested up to complex conjugation

Self-testing refers to the certification of quantum states and measurements based entirely on the correlations exhibited by measurements on separate subsystems. In the bipartite case, self-testing of states has been completely characterized, up to local isometries, as there exist protocols that self-test arbitrary pure states of any local dimension. Much less is known in the multipartite case, where an important difference with respect to the bipartite case appears: there exist multipartite states that are not equivalent, up to local isometries, to their complex conjugate. Thus, any self-testing characterization must in general be complete up to not only local unitaries, but also complex conjugation. Under these premises, in this work, we give a complete characterization of self-testing in the multipartite qubit case.