Systematic and statistical errors in homodyne measurements of the density matrix

We study both systematic and statistical errors in radiation density matrix measurements. First we estimate the minimum number of scanning phases needed to reduce systematic errors to below a fixed threshold. Then, we calculate the statistical errors, intrinsic in the procedure that gives the density matrix. We present a detailed study of such errors versus the detectors' quantum efficiency eta and the matrix indices in the number representation, for different radiation states. For unit quantum efficiency, and for both coherent and squeezed states, the statistical errors of the diagonal matrix elements saturate for large n. In contrast, off-diagonal errors increase with the distance from the diagonal. For non-unit quantum efficiency the statistical errors along the diagonal do not saturate and increase dramatically versus both 1 - eta and the matrix indices.