  We report an experimental realization of an adaptive quantum state tomography
protocol. Our method takes advantage of a Bayesian approach to statistical
inference and is naturally tailored for adaptive strategies. For pure states we
observe close to 1/N scaling of infidelity with overall number of registered
events, while best non-adaptive protocols allow for $1/\sqrt{N}$ scaling only.
Experiments are performed for polarization qubits, but the approach is readily
adapted to any dimension.
