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.

• Received 14 May 2002

DOI:https://doi.org/10.1103/PhysRevLett.89.277904