SIGNAL-TO-NOISE RATIO OF PREAMPLIFIED HOMODYNE DETECTION IN QUANTUM TOMOGRAPHY

The operational theory of homodyne detection by nonideal detectors, us ed in quantum tomography, was recently modified in order to incorporat e the preamplification (before homodyne detection) of the input signal , thus enabling one to beat the handicap of the lower than 0.5 detecto r efficiency. In the present work we set expressions for the Mandel Q parameter and the signal-to-noise ratio in terms of the operational (m easured) moments of the preamplified homodyne detection formalism. The se quantities furnish important information on the statistical propert ies of the input signal field and the photocounts at the output. We il lustrate the theory by considering several kinds of fields (for the in put signal) and determine the effects of the preamplification on the o utput signal-to-noise ratios. Here we essentially verify that (i) the preamplification shifts the statistics towards the super-Poissonian li mit, without jeopardizing the capacity of reconstructing a sub-Poissio nan input signal, and (ii) the preamplification is more effective, i.e ., the rate of increase of the signal-to-noise ratio of the output pho tocount is larger for low-efficiency detectors than for ideal ones.