UNIFIED TREATMENT OF HETERODYNE DETECTION: THE SHAPIRO–WAGNER AND CAVES FRAMEWORKS

Abstract

A comparative study is performed on two heterodyne systems of photon detectors expressed in terms of a signal annihilation operator and an image band creation operator called Shapiro–Wagner and Caves' frame, respectively. This approach is based on the introduction of a convenient operator [Formula: see text] which allows a unified formulation of both cases. For the Shapiro–Wagner scheme, where [Formula: see text], quantum phase and amplitude are exactly defined in the context of relative number state (RNS) representation, while a procedure is devised to handle suitably and in a consistent way Caves' framework, characterized by [Formula: see text], within the approximate simultaneous measurements of noncommuting variables. In such a case RNS phase and amplitude make sense only approximately.