Moreover, it is well known that due to statistical fluctuations and systematic errors the density matrix obtained from the measured state by linear inversion is not positive semidefinite and it has some negative eigenvalues. An important step in a typical tomography is fitting a physical, i. e., positive semidefinite density matrix on the tomographic data. This step often represents a bottleneck in the overall process in full state tomography. However, PI tomography, as we have just discussed, allows the density matrix to be stored much more efficiently, which also allows an efficient fitting using convex optimization, which also guarantees that the solution is a global optimum.