TOMOGRAPHIC RECONSTRUCTION OF THE DENSITY-MATRIX VIA PATTERN FUNCTIONS

We propose a general method for reconstructing directly the density ma trix of a single light mode in optical homodyne tomography. In our sch eme the density matrix [a\<(rho)over cap>\a'] is obtained by averaging a set of pattern functions F-aa'(x(theta), theta) with respect to the homodyne data x(theta). The functions show the typical features of th e quadrature distributions for the corresponding density-matrix elemen ts. It is also possible to compensate the effect of detection losses w hich requires, however, extra effort in both experimental and numerica l precision. We calculate the pattern functions for the coherent-state and Pock representations and study their properties. We believe that our method is the most efficient way for reconstructing the density ma trix from homodyne measurements.