Self-learning estimation of quantum states

We report the experimental estimation of arbitrary qubit states 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). Two hyperfine states of a single trapped ${}^{171}{\mathrm{Yb}}^{+}$ ion serve as a qubit. It is demonstrated that the difference in fidelity between this adaptive strategy and passive strategies increases in the presence of decoherence.