Optimized optical tomography of quantum states of a room-temperature alkali-metal vapor

We demonstrate an experimental technique for the quantum-state tomography of the collective qutrit states of a room-temperature alkali-metal vapor. It is based on the measurements of the polarization of light traversing the vapor subjected to a magnetic field. To assess the technique's robustness against errors, experimental investigations are supported with numerical simulations. This not only allows us to determine the fidelity of the reconstructed states, but also to analyze the quality of the reconstruction for specific experimental parameters, such as light tuning and the number of measurements. By utilizing the conditional number, we demonstrate that the reconstruction robustness can be optimized by a proper adjustment of experimental parameters, and further improvement is possible with the repetition of specific measurements. Our results demonstrate the potential of this high-fidelity reconstruction method of quantum states of room-temperature atomic vapors.