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 [Formula presented] identical copies. We give explicit examples for low [Formula presented]. For large [Formula presented], we show that the fidelity saturates the collective measurement bound up to order [Formula presented]. When the signal state lays on a meridian of the Bloch sphere, we show that this can be achieved without classical communication. © 2002 The American Physical Society.