Encoding the information in relative parameters

We investigate the problem of communicating three parameters in the absence of shared reference frame. We explore two methods in which the relative angles of spins are used to encode the parameters. In the first method we use three spins that carry the information in their relative angles while in the second method we use three disjoint spin-pairs and the information is sent through the relative angles of each individual pair. We show that in the first method, the information conveyed by each qubit is more than the second one, and that is while it requires fewer particles.