  In this article, we investigate the problem of state reconstruction of
four-level quantum systems. A realistic scenario is considered with measurement
results distorted by random unitary operators. Two frames which define
injective measurements are applied and compared. By introducing arbitrary
rotations, we can test the performance of the framework versus the amount of
experimental noise. The results of numerical simulations are depicted on graphs
and discussed. In particular, a class of entangled states is reconstructed. The
concurrence is used as a figure of merit in order to quantify how well
entanglement is preserved through noisy measurements.
