Quantum Phase Measurement

Abstract

Theory of feasible quantum phase mesurement is formulated within the framework of quantum estimation theory. Phase detection is linked to the measurement of a pair of commuting Hermitian operators. The ideal phase concepts are distinguished, among all the possible realizations as the representations of the Euclidean algebra on Hermitian operators. Possible representations of the rotational subgroup correspond to measurements with indefinite phase. Traditional “quantum phase difficulties”, ascribed sometimes to the lack of uniqueness of the Hermitian phase operator, are related to the classical attempt to distinguish between quantum effect and measurement itself. In realistic quantum phase measurement, the phase statistics should be estimated using counted discrete data. Possible interferometric measurements of phase-so called operationally defined quantum phase models-are included as special realizations of presented theory.