  It has been recently shown (Bartlett et al. 2003) 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 article 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.
