A necessary and sufficient condition for minimum phase and implications for phase retrieval

We give a necessary and sufficient condition for a function E(t) being of minimum phase, and hence for its phase being univocally determined by its intensity |E(t)|. This condition is based on the knowledge of E(t) alone and not of its analytic continuation in the complex plane, thus greatly simplifying its practical applicability. We apply these results to find the class of all band-limited signals that correspond to distinct receiver states when the detector is sensitive to the field intensity only and insensitive to the field phase, and discuss the performance of a recently proposed transmission scheme able to linearly detect all distinguishable states.