  Quantum state tomography (QST) is a crucial ingredient for almost all aspects
of experimental quantum information processing. As an analog of the "imaging"
technique in the quantum settings, QST is born to be a data science problem,
where machine learning techniques, noticeably neural networks, have been
applied extensively. In this work, we build an integrated all-optical setup for
neural network QST, based on an all-optical neural network (AONN). Our AONN is
equipped with built-in nonlinear activation function, which is based on
electromagnetically induced transparency. Experiment results demonstrate the
validity and efficiency of the all-optical setup, indicating that AONN can
mitigate the state-preparation-and-measurement error and predict the phase
parameter in the quantum state accurately. Given that optical setups are highly
desired for future quantum networks, our all-optical setup of integrated
AONN-QST may shed light on replenishing the all-optical quantum network with
the last brick.
