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