  Quantum tomography is a widely applicable method for reconstructing unknown
quantum states and processes. However, its applications in quantum technologies
usually also require estimating the difference between prepared and target
quantum states with reliable confidence intervals. In this work we suggest a
computationally efficient and reliable scheme for determining well-justified
error bars for quantum tomography. We approximate the probability distribution
of the Hilbert-Schmidt distance between the target state and the estimation,
which is given by the linear inversion, by calculating its two moments. We also
present a generalization of this approach for quantum process tomography and
deriving confidence intervals for affine functions. We benchmark our approach
for a number of quantum tomography protocols using both simulation and
demonstration with the use of a cloud-accessible quantum processor. The
obtained results pave the way for the use of the suggested scheme for the
complete characterization of quantum systems of various natures.
