  The optimal estimation of a quantum mechanical 2-state system (qubit) - with
N identically prepared qubits available - is obtained by measuring all qubits
simultaneously in an entangled basis. We report the experimental estimation of
qubits using a succession of N measurements on individual qubits where the
measurement basis is changed during the estimation procedure conditioned on the
outcome of previous measurements (self-learning estimation). The performance of
this adaptive algorithm is compared with other algorithms using measurements in
a factorizing basis.
