Signal-to-noise ratio of preamplified homodyne detection in quantum tomography
Marcelo A. Marchiolli, S. S. Mizrahi, V. V. Dodonov · Physical Review A · 1998
The operational theory of homodyne detection by nonideal detectors, used in quantum tomography, was recently modified in order to incorporate the preamplification (before homodyne detection) of the input signal, thus enabling one to beat the handicap of the lower than 0.5 detector efficiency. In the present work we set expressions for the Mandel $Q$ parameter and the signal-to-noise ratio in terms of the operational (measured) moments of the preamplified homodyne detection formalism. These quantities furnish important information on the statistical properties of the input signal field and the photocounts at the output. We illustrate the theory by considering several kinds of fields (for the input signal) and determine the effects of the preamplification on the output signal-to-noise ratios. Here we essentially verify that (i) the preamplification shifts the statistics towards the super-Poissonian limit, without jeopardizing the capacity of reconstructing a sub-Poissionan input signal, and (ii) the preamplification is more effective, i.e., the rate of increase of the signal-to-noise ratio of the output photocount is larger for low-efficiency detectors than for ideal ones.