Optimal Scheme for Estimating a Pure Qubit State via Local Measurements

We present the optimal scheme for estimating a pure qubit state by means of local measurements on $N$ identical copies. We give explicit examples for low $N$. For large $N$, we show that the fidelity saturates the collective measurement bound up to order $1/N$. When the signal state lays on a meridian of the Bloch sphere, we show that this can be achieved without classical communication.