Figure 1

Quantum state tomography with two-step adaptive strategy. The observables ${\mathit{\sigma }}_x^{\prime }$, ${\mathit{\sigma }}_y^{\text{'}}$ and ${\sigma }_z^{\text{'}}$ depend on the estimator ${\hat{\rho }}_1$ obtained in the first step and are related to σ_x, σ_y and σ_z via the unitary transformation $U\left({\stackrel{\mathit{ˆ}}{\mathit{s}}}_1\right)$ described in the main text. The probabilities p₁, p₂ and p₃ depend on both the estimator ${\hat{\rho }}_1$ and the figure of merit. In the large N limit, it suffices to use the measurement statistics of step 2 to construct the second MLE. In practice, it is preferable to use the measurement statistics of both steps.