Abstract
Even though heralded single-photon sources have been generated routinely through spontaneous parametric down conversion, vacuum and multiple photon states are unavoidably involved. With machine learning, we report the experimental implementation of photon number state tomography by directly estimating target parameters. Compared to the Hanbury Brown and Twiss measurements only with clicked events recorded, our neural-network-enhanced quantum-state tomography characterizes the photon number distribution for all possible photon number states from the balanced homodyne detectors. By using the histogram-based architecture, a direct parameter estimation on the negativity in Wigner's quasiprobability phase space is demonstrated. Such a fast, robust, and precise quantum-state tomography provides us a crucial diagnostic toolbox for the applications with incoherent mixture of Fock states.