Mode optimization for quantum-state tomography with array detectors

We demonstrate that it is possible to choose an optimal signal mode for state reconstruction when performing quantum-state tomography with array detectors. The mode optimization is done during the data analysis (i.e., after all the data have been collected.) We develop theoretically a procedure for finding the mode that satisfies a criterion which is quadratic in field operators; as examples we explicitly show how to maximize the average photon number, or the amount of quadrature squeezing. We experimentally demonstrate the technique by finding the mode which maximizes the average photon number for coherent-state signal beams occupying both linear and sinusoidal modes.