Relative information encoded in the degree of entanglement to discriminate bipartite states

It has been recently shown [S.D. Bartlett, T. Rudolph, R.W. Spekkens, Phys. Rev. Lett. 91 (2003) 027901] that information encoded into relative degrees of freedom enables communication without a common reference frame using entangled bipartite states. In this case the relative information stored in the two-qubit system is shared between the polarization degrees of freedom and the degree of entanglement. In the present Letter a specific state discrimination problem is envisioned where the degree of entanglement carries the only relative parameter, so that certain maximally entangled states are perfectly distinguishable, while discrimination of product states is impossible.