A scheme for the reconstruction of two-mode SU(1,1) states using parametric amplifiers is proposed. The probability of the output state being in a certain two-mode number state is measured. The probability data are then converted to extract the density matrix of the input state by taking advantage of certain asymmetries in the input state. It is shown that this inversion can be achieved by the least-squares method after singular value decomposition of the design matrix followed by Tikhonov regularization.
