Quantum Limit Characterization of Signal-to-Noise Ratio using Phase- Shift Keying in Homodyne Detection

Jeffrey H. Shapiro, N. C. Wong

Recently, there has been some controversy concerning the role of signal-to-noise ratio (SNR) calculations in conjunction with optical amplifiers and phase-shift keying. Analysis has shown that the large-signal SNR at the output of an optical parametric amplifier (OPA) or optical parametric oscillator (OPO) can exceed the shot-noise limit when an injected signal beam is used to elicit small-signal gain saturation. Although no small-signal SNR gain is obtained in this way, the large-signal SNR improvement does translate into a communication performance improvement if binary phase-shift keying is applied to the resulting output beam. Analysis has also shown that the large-signal, shot-noise limited SNR can be exceeded when a binary phase-shift keyed coherent-state beam is applied to a preamplify-feedforward-homodyne receiver. In this case, however, there is no communication performance improvement. Indeed, the preamplify-feed-forward-homodyne receiver requires twice as many signal photons, on average, to equal the error probability of ordinary homodyne detection. In this talk we will show that there is no contradiction between these two examples.

R. Loudon

Marcelo A. Marchiolli, Salomon Sylvain Mizrahi, V. V. Dodonov

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.

Nigel G. Walker, J.E. Carroll

Stefano Olivares, S. Cialdi, F. Castelli +1 more

We address binary optical communication channels based on phase-shift-keyed coherent signals in the presence of phase diffusion. We prove theoretically and demonstrate experimentally that a discrimination strategy based on homodyne detection is robust against this kind of noise for any value of the channel energy. Moreover, we find that a homodyne receiver beats the performance of a Kennedy receiver as the signal energy increases and achieves the Helstrom bound in the limit of large noise.

Horace P. Yuen, Jeffrey H. Shapiro