It was just recently that the problem of quantum tomography has been called to the attention of the statistical community throughout the proof of consistency results for Projection Pattern Function and Sieve Maximum Likelihood estimators of the density matrix and the Wigner function of the quantum state of light. Proving consistency means that the estimator converges to the desired state in appropriate norm. A step further in this study is to prove how fast (rate of convergence) an estimator converges as the number of samples increases. We show pointwise rates of convergence of the minimax error for the classical Kernel estimator of the Wigner function from quantum homodyne tomography data, assuming the Wigner function is in certain class. As a whole, we also give an overview of previous works and motivate future directions.