Communication of spin directions with product states and finite measurements - art. no. 022305

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.