PHASE-INTENSITY UNCERTAINTY RELATION FROM QUASI-PROBABILITY DISTRIBUTIONS

Extending the concept of Wehrl's entropy to s-parametrized quasiprobab ility distributions, as they are observed in optical homodyne detectio n with realistic detectors, we show that the marginal entropies with r espect to phase and amplitude obey a rigourous inequality relation. Re lating those entropies to phase and intensity uncertainties, respectiv ely, we arrive at an uncertainty relation for operationally defined ph ase and intensity that takes explicit account of the noise introduced by non-ideal detectors.