Quantum phase distribution by operator synthesis

Abstract

Methods proposed so far for measuring the canonical phase probability distribution of light are very difficult to implement. In particular the method of projection synthesis, which synthesizes a phase state projector, involves the use of a beam splitter and a specially engineered reference state. Here we extend this method by use of an additional beam splitter to synthesize phase sine and cosine operators. This allows the measurement of all the moments needed to construct the phase distribution. The reference state required for operator synthesis is, remarkably, just an easily prepared coherent state.