A note on the measurement of phase space observables with an eight-port homodyne detector

TL;DR

This paper demonstrates that an eight-port homodyne detector can measure a wide range of phase space observables, not just the Husimi Q-function, using a rigorous quantum approach without classicality assumptions.

Contribution

It proves that all phase space observables can be obtained as high amplitude limits of measurements from an eight-port homodyne detector, extending previous results.

Findings

Any phase space observable can be measured with an eight-port homodyne detector.

The measurement of these observables does not rely on classicality assumptions.

The results are supported by recent rigorous quantum theory of homodyne detection.

Abstract

It is well known that the Husimi Q-function of the signal field can actually be measured by the eight-port homodyne detection technique, provided that the reference beam (used for homodyne detection) is a very strong coherent field so that it can be treated classically. Using recent rigorous results on the quantum theory of homodyne detection observables, we show that any phase space observable, and not only the Q-function, can be obtained as a high amplitude limit of the signal observable actually measured by an eight-port homodyne detector. The proof of this fact does not involve any classicality assumption.