After an introduction to the notion of quantum generative adversarial networks (qGANs), I will summarize a recent quantum tomography protocol for constructing a classical estimate of a quantum state by performing repeated measurements on a n-qubit system. I will then discuss the convergence of the protocol with respect to a quantum version of the first-order Wasserstein distance, inspired by the theory of optimal mass transport. In particular, I will show how this convergence result allows us to conclude that a qGAN can be equivalently trained using classical estimators of quantum states instead of quantum data. This fact is important in practice, as it enables the training of quantum models without requiring direct access to quantum memory or coherent quantum data streams.