Witnessing entanglement of remote particles with incomplete teleportation

Having common reference frames or aligned coordinate systems is one of the presumptions in witnessing entanglement in a two-party state possessed by two remote parties. This assumption may fail for many reasons. With an unlimited supply of singlet states, the two parties can first align their coordinate systems and then measure any entanglement witness. In this paper, we propose an alternative method which uses the same resource for incomplete teleportation of states between the two parties, enabling them to witness the entanglement of any shared state by local measurements without the need for prior alignment of the coordinate systems. The method works for any kind of witness and in any dimension. Beyond the context of entanglement witnesses, our method works also for remote measurements of observables of particles (entangled or not) in laboratories which may have deficiency in their resources.