  Total spin eigenstates can be used to intrinsically encode a direction, which
can later be decoded by means of a quantum measurement. We study the optimal
strategy that can be adopted if, as is likely in practical applications, only
product states of $N$-spins are available. We obtain the asymptotic behaviour
of the average fidelity which provides a proof that the optimal states must be
entangled. We also give a prescription for constructing finite measurements for
general encoding eigenstates.
