Optical homodyne detection in view of joint probability distribution

TL;DR

This paper investigates optical homodyne detection through joint probability distributions, clarifying phase localization and invariance properties, which underpin quantum-state tomography and the use of coherent states.

Contribution

It provides a detailed analysis of the phase invariance and joint probability distribution in homodyne detection, offering new insights into the theoretical foundations of optical quantum measurements.

Findings

Homodyne detection exhibits phase invariance under certain transformations.

Joint probability distributions reveal phase localization mechanisms.

Theoretical clarification supports the use of coherent states in quantum optics.

Abstract

Optical homodyne detection is examined in view of joint probability distribution. It is usually discussed that the relative phase between independent laser fields are localized by photon-number measurements in interference experiments such as homodyne detection. This provides reasoning to use operationally coherent states for laser fields in the description of homodyne detection and optical quantum-state tomography. Here, we elucidate these situations by considering the joint probability distribution and the invariance of homodyne detection under the phase transformation of optical fields.