Entangled Quantum States as Direction Indicators

We consider the use of $N$ spin- $\frac{1}{2}$ particles for indicating a direction in space. If $N>\mathrm{}2\mathrm{}$, their optimal state is entangled. For large $N$, the mean square error decreases as $N^{-2\mathrm{}}$ (rather than $N^{-1\mathrm{}}$ for parallel spins).