  We propose a quantum tomography scheme for pure qudit systems which adopts
random base measurements and generative learning methods, along with a built-in
fidelity estimation approach to assess the reliability of the tomographic
states. We prove the validity of the scheme theoretically, and we perform
numerically simulated experiments on several target states including three
typical quantum information states and randomly initiated states, demonstrating
its efficiency and robustness. The number of replicas required by a certain
convergence criterion grows in the manner of low-degree polynomial when the
system scales, thus the scheme achieves high scalability that is crucial for
practical quantum state tomography.

Quantum Physics