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

We provide a simple analytic relation that connects the density operator (p) over cap of the electromagnetic field with the tomographic homodyne probabilities for generic quantum efficiency eta of detectors. The 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 possible 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, which otherwise would be smeared out by inefficient detection.