  Suppose, we are given two finite ensembles of pure qubit states, so that the
qubits in each ensemble are prepared in identical (but unknown for us) states
lying on the equator of the Bloch sphere. What is the best strategy to estimate
fidelity between these two finite ensembles of qubit states? We discuss three
possible strategies for the fidelity estimation. We show that the best strategy
includes two stages: a specific unitary transformation on two ensembles and
state estimation of the output states of this transformation.

Quantum Physics