HOMODYNE DETECTION OF THE DENSITY-MATRIX OF THE RADIATION-FIELD

We provide a simple analytic relation that connects the density operat or (p) over cap of the electromagnetic field with the tomographic homo dyne probabilities for generic quantum efficiency eta of detectors. Th e problem of experimentally ''sampling'' a general matrix element [psi \(p) over cap\phi] is addressed in the statistically rigorous sense of the central-limit theorem. We show that experimental sampling is poss ible also for nonunit efficiency, provided that eta satisfies a lower bound related to the ''resolutions'' of vectors \psi] and \phi] in the quadrature representations. For coherent and number states the bound is eta>1/2. On the basis of computer-simulated experiments we show the feasibility of detecting delicate quantum probability oscillations, w hich otherwise would be smeared out by inefficient detection.