Fast Quantum State Tomography Implemented by Measurement Axis Adjustment

We developed a fast quantum state tomography method by choosing three independent measurement axes based on the initial statistical sampling of qubit state measurements. The measurement standard deviation (SD) is inversely proportional to the square roots of N, the number of readout, and proportional to the square roots of p(1-p) where p is a probability that state readout results in 0 (or 1). Accordingly, a straightforward way of reducing SD is to increase N which requires a large number of state-readout. An alternative way is to adjust measurement axes and, thus, modify the probability p of state readout. After the adjustment, we were able to obtain the equal error bound of SD with only 2/3 of N required previously. This method is independent of the 0/1 state resolution of the system. Therefore, the worse the system resolution, the more the required number of readout decrease.