Communication of Spin Directions with Product States and Finite Measurements

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Abstract
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.

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