  Resource-efficient quantum state tomography is one of the key ingredients of
future quantum technologies. In this work, we propose a new tomography protocol
combining standard quantum state reconstruction methods with an attention-based
neural network architecture. We show how the proposed protocol is able to
improve the averaged fidelity reconstruction over linear inversion and
maximum-likelihood estimation in the finite-statistics regime, reducing at
least by an order of magnitude the amount of necessary training data. We
demonstrate the potential use of our protocol in physically relevant scenarios,
in particular, to certify metrological resources in the form of many-body
entanglement generated during the spin squeezing protocols. This could be
implemented with the current quantum simulator platforms, such as trapped ions,
and ultra-cold atoms in optical lattices.

Quantum Physics;Quantum Gases