Effective and robust quantum state tomography of electron-nuclear spins in diamond by time-resolved fluorescence

Quantum state tomography (QST) of electron-nuclear spins of nitrogen-vacancy (NV) center in diamond commonly requires a sequence of population flipping operations and frequent calibration of basis states by fluorescence photon-counting. Here, we realize an effective and robust quantum state tomography of electron-nuclear spins based on time-resolved fluorescence, which can enhance the signal-to-noise ratio between different basis states up to 29.6% compared to the photon-counting method. Meanwhile, our method can directly obtain the population of four basis states with only one measurement, which significantly improves the efficiency of tomography. Furthermore, the photon count rate fluctuation of time-resolved fluorescence can be reduced to the standard quantum limit by normalization operation, indicating that the time-resolved method is calibration-free. This method could be easily applied to multi-nuclear spins of NV center in diamond and extended to other solid-state spin systems.